Need suggestions for poll 'options' for Miss Jade

[Shankara20]

lmao..........hmmmn Sir Shank........would Miss Jade be wearing pumps or sneakers reciting this piece. Has a sort of Cheerleader on acid type flare to it .......smiles sweetly

good point Sister Rebecca, I pull that from consideration and will see what else I might find.



errrr, could she do it with pom poms?

 

[shy slave]

1 of 4 suggestions

There are so many pieces to choose from, could have filled a thread all by myself lol

Ok, please bear with me on this first suggestion.
It comes from Macbeth and its a speech by Hecat who is the witch of all witches.
She is angry that the three witches have been meddling with Macbeths mind. It transpires she is angry because she was not included and Macbeth wasn't worth their efforts. But as the process has started she wants in on the act and plans to confuse him further by playing on his own weaknesses.

This speech makes me think of a Hierarchical subbmissive society, the alpha sub being Hecat and the three witches she is addressing the additional submissives; Macbeth would be the Dom they are playing mind fuck games with, whilst he continues to think he is in control.
It seems the ultimate topping from the bottom.

I know your now wondering what I am smoking/drinking/ingesting in some form to give these thoughts.
Well its just how my mind wanders....I hope it comes back lol

Macbeth Act III.4
Have I not reason, bedlams as you are
saucy and overbold? How did you dare
To trade and traffic with macbeath
In riddles and affairs of death,
And I, the mistress of your charms,
The close contriver of all harms
Was never called to bear my part
Or show the glory of our Art?
And which is worse, all you have done
Hath been but for a wayward son,
Spiteful and wrathful who, as others do,
Loves for his own ends, and not for you
But make amends now, get you gone
And at the pit of Acheron
Meet me i’the morning. Thither he
Will come to know his destiny.
Your vessels and your spells provide,
Your charms and everything besides.
I am for the air; this night I’ll spend
Unto a dismal and a fatal end.
Great business must be wrought ere noon
Upon the corner of the moon:
There, hangs the vaporous drop profound;
I’ll catch it ere it comes to ground;
And that distilled by magic sleights
Shall raise such artificial sprites
As by the strength of this illusion
Shall draw him on in his confusion.
He shall spurn fate, scorn death and bear
His hopes ‘bove wisdom, grace and fear
And you all know security
Is mortals chiefest enemy.

 

[babiesmiles]

Fantastic piece Shy !

 

[shy slave]

I love poetry so I am using this as an excuse to indulge.
As Miss Jade is apart from him right now my thoughts turned romantic, I had to search to find these as my preference is grief and loss poetry.

This one is beautiful, and really reminded me of that surge of passion you get when you see him and how it feels when he is far away. It talks of selfish love yet she says she would sit at his feet and serve him. It's a measure of submission when the author want so much the simple pleasure of being in his presence that she describes it as selfish.

A Woman's Love
Ella Wheeler Wilcox
So vast the tide of Love within me surging,
It overflows like some stupendous sea,
The confines of the Present and To-be;
And 'gainst the Past's high wall I feel it urging,
As it would cry "Thou too shalt yield to me!"
All other loves my supreme love embodies;
I would be she on whose soft bosom nursed
Thy clinging infant lips to quench their thirst;
She who trod close to hidden worlds where God is,
That she might have, and hold, and see thee first.
I would be she who stirred the vague fond fancies,
Of thy still childish heart; who through bright days
Went sporting with thee in the old-time plays,
And caught the sunlight of thy boyish glances
In half-forgotten and long-buried Mays.
Forth to the end, and back to the beginning,
My love would send its inundating tide,
Wherein all landmarks of thy past should hide.
If thy life's lesson must be learned through sinning,
My grieving virtue would become thy guide.
For I would share the burden of thy errors,
So when the sun of our brief life had set,
If thou didst walk in darkness and regret,
E'en in that shadowy world of nameless terrors,
My soul and thine should be companions yet.
And I would cross with thee those troubled oceans
Of dark remorse whose waters are despair:
All things my jealous reckless love would dare,
So that thou mightst not recollect emotions
In which it did not have a part and share.
There is no limit to my love's full measure,
Its spirit gold is shaped by earth's alloy;
I would be friend and mother, mate and toy,
I'd have thee look to me for every pleasure,
And in me find all memories of joy.
Yet though I love thee in such selfish fashion,
I would wait on thee, sitting at thy feet,
And serving thee, if thou didst deem it meet.
And couldst thou give me one fond hour of passion,
I'd take that hour and call my life complete.

 

[shy slave]

This one is sweet, it talks about non-sexual pleasures in life yet when I read it I feel there is a passion for life that can only be found when exploring with yourself.
A reminder that we do not need others, they enhance all we have but there are other things to have a passion for.
Again as Miss Jade is apart from him, its a reminder that we continue to live and love life whilst waiting for their return.

Pleasure Charlotte Bronte
(A Short Poem or Else Not Say I)
True pleasure breathes not city air,
Nor in Art's temples dwells,
In palaces and towers where
The voice of Grandeur dwells.
No! Seek it where high Nature holds
Her court 'mid stately groves,
Where she her majesty unfolds,
And in fresh beauty moves;
Where thousand birds of sweetest song,
The wildly rushing storm
And hundred streams which glide along,
Her mighty concert form!
Go where the woods in beauty sleep
Bathed in pale Luna's light,
Or where among their branches sweep
The hollow sounds of night.
Go where the warbling nightingale
In gushes rich doth sing,
Till all the lonely, quiet vale
With melody doth ring.
Go, sit upon a mountain steep,
And view the prospect round;
The hills and vales, the valley's sweep,
The far horizon bound.
Then view the wide sky overhead,
The still, deep vault of blue,
The sun which golden light doth shed,
The clouds of pearly hue.
And as you gaze on this vast scene
Your thoughts will journey far,
Though hundred years should roll between
On Time's swift-passing car.
To ages when the earth was young,
When patriarchs, grey and old,
The praises of their god oft sung,
And oft his mercies told.
You see them with their beards of snow,
Their robes of ample form,
Their lives whose peaceful, gentle flow,
Felt seldom passion's storm.

 

[shy slave]

There is something slightly naff about Desiderata, but there remain parts of it which have meaning at different times in our lives. People of a certain age probably had this as a poster on their wall at sometime in their life too

Desiderata
Max Ehrmann
Go placidly amid the noise and haste, and remember what peace there may be in silence.
As far as possible, without surrender, be on good terms with all persons.
Speak your truth quietly and clearly; and listen to others,
even to the dull and ignorant; they too have their story.
Avoid loud and aggressive persons, they are vexations to the spirit.
If you compare yourself with others, you may become vain and bitter,
for always there will be greater and lesser persons than yourself.
Enjoy your achievements as well as your plans.
Keep interested in your own career, however humble;
it is a real possession in the changing fortunes of time.
Exercise caution in your business affairs, for the world is full of trickery.
But let this not blind you to what virtue there is;
many persons strive for high ideals,
and everywhere life is full of heroism.
Be yourself. Especially do not feign affection. Neither be cynical about love;
for in the face of all aridity and disenchantment it is as perennial as the grass.
Take kindly the counsel of the years, gracefully surrendering the things of youth.
Nurture strength of spirit to shield you in sudden misfortune.
But do not distress yourself with dark imaginings.
Many fears are born of fatigue and loneliness.
Beyond a wholesome discipline, be gentle with yourself.
You are a child of the universe no less than the trees and the stars;
you have a right to be here. And whether or not it is clear to you,
no doubt the universe is unfolding as it should.
Therefore be at peace with God, whatever you conceive Him to be.
And whatever your labors and aspirations, in the noisy confusion of life,
keep peace with your soul. With all its sham, drudgery and broken dreams,
it is still a beautiful world. Be cheerful. Strive to be happy.

 

[@}-}rebecca----]

There are so many pieces to choose from, could have filled a thread all by myself lol

Ok, please bear with me on this first suggestion.
It comes from Macbeth and its a speech by Hecat who is the witch of all witches.
She is angry that the three witches have been meddling with Macbeths mind. It transpires she is angry because she was not included and Macbeth wasn't worth their efforts. But as the process has started she wants in on the act and plans to confuse him further by playing on his own weaknesses.

This speech makes me think of a Hierarchical subbmissive society, the alpha sub being Hecat and the three witches she is addressing the additional submissives; Macbeth would be the Dom they are playing mind fuck games with, whilst he continues to think he is in control.
It seems the ultimate topping from the bottom.

I know your now wondering what I am smoking/drinking/ingesting in some form to give these thoughts.
Well its just how my mind wanders....I hope it comes back lol

Ohhh Miss Shy true to your word a superb selection, ohh hope Miss Jades tattoo was realllllllllllllll painful and she has hugeeeeeeeeeeee endorphins because she is going to freak out the length of some of these.......

Looks at time ........hmmn not long to go now.........bites lip...oh yeah

 

[jadefirefly]

*slips in quietly*
*offers much-practiced curtsey to Miss Rebecca*

The tattoo was indeed rather unpleasant today... fortunately the majority of the work was on the right side of my back, which doesn't hurt as badly.

These are really very long! But yours was a doozy too, so I can't really complain. And isn't Jabberwocky a long poem too? I can't promise I'm any good with that much to remember, but I'll do my best!

On that note I think I'll slip out and peek at that link.

*excuses self*

 

[@}-}rebecca----]

*slips in quietly*
*offers much-practiced curtsey to Miss Rebecca*

The tattoo was indeed rather unpleasant today... fortunately the majority of the work was on the right side of my back, which doesn't hurt as badly.

These are really very long! But yours was a doozy too, so I can't really complain. And isn't Jabberwocky a long poem too? I can't promise I'm any good with that much to remember, but I'll do my best!

On that note I think I'll slip out and peek at that link.

*excuses self*

ummmn Jabberwocky isn't that long .......runs

 

[jadefirefly]

Iiiiii'm just throwing stuff in here for fun. Nobody mind me.
---------

I amar prestar aen. The world is changed. Han matho ne nen. I feel it in the water. Han mathon ned cae. I feel it in the earth. A han noston ned gwilith. I smell it in the air. Much that once was is lost, for none now live who remember it.
It began with the forging of the Great Rings. Three were given to the Elves, immortal, wisest and fairest of all beings. Seven to the Dwarf-Lords, great miners and craftsmen of the mountain halls. And nine, nine rings were gifted to the race of Men, who above all else desire power. For within these rings was bound the strength and the will to govern each race. But they were all of them deceived, for another ring was made. Deep in the land of Mordor, in the Fires of Mount Doom, the Dark Lord Sauron forged a master ring, and into this ring he poured his cruelty, his malice and his will to dominate all life. One ring to rule them all.
One by one, the free lands of Middle-Earth fell to the power of the Ring, but there were some who resisted. A last alliance of men and elves marched against the armies of Mordor, and on the very slopes of Mount Doom, they fought for the freedom of Middle-Earth. Victory was near, but the power of the ring could not be undone.
It was in this moment, when all hope had faded, that Isildur, son of the king, took up his father's sword.
Sauron, enemy of the free peoples of Middle-Earth, was defeated. The Ring passed to Isildur, who had this one chance to destroy evil forever, but the hearts of men are easily corrupted. And the ring of power has a will of its own. It betrayed Isildur, to his death.
And some things that should not have been forgotten were lost. History became legend. Legend became myth. And for two and a half thousand years, the ring passed out of all knowledge. Until, when chance came, it ensnared another bearer.
It came to the creature Gollum, who took it deep into the tunnels of the Misty Mountains. And there it consumed him. The ring gave to Gollum unnatural long life. For five hundred years it poisoned his mind, and in the gloom of Gollum's cave, it waited. Darkness crept back into the forests of the world. Rumor grew of a shadow in the East, whispers of a nameless fear, and the Ring of Power perceived its time had come. It abandoned Gollum, but then something happened that the Ring did not intend. It was picked up by the most unlikely creature imaginable: a hobbit, Bilbo Baggins, of the Shire.
For the time will soon come when hobbits will shape the fortunes of all.

 

[@}-}rebecca----]

Iiiiii'm just throwing stuff in here for fun. Nobody mind me.
---------

I amar prestar aen. The world is changed. Han matho ne nen. I feel it in the water. Han mathon ned cae. I feel it in the earth. A han noston ned gwilith. I smell it in the air. Much that once was is lost, for none now live who remember it.
It began with the forging of the Great Rings. Three were given to the Elves, immortal, wisest and fairest of all beings. Seven to the Dwarf-Lords, great miners and craftsmen of the mountain halls. And nine, nine rings were gifted to the race of Men, who above all else desire power. For within these rings was bound the strength and the will to govern each race. But they were all of them deceived, for another ring was made. Deep in the land of Mordor, in the Fires of Mount Doom, the Dark Lord Sauron forged a master ring, and into this ring he poured his cruelty, his malice and his will to dominate all life. One ring to rule them all.
One by one, the free lands of Middle-Earth fell to the power of the Ring, but there were some who resisted. A last alliance of men and elves marched against the armies of Mordor, and on the very slopes of Mount Doom, they fought for the freedom of Middle-Earth. Victory was near, but the power of the ring could not be undone.
It was in this moment, when all hope had faded, that Isildur, son of the king, took up his father's sword.
Sauron, enemy of the free peoples of Middle-Earth, was defeated. The Ring passed to Isildur, who had this one chance to destroy evil forever, but the hearts of men are easily corrupted. And the ring of power has a will of its own. It betrayed Isildur, to his death.
And some things that should not have been forgotten were lost. History became legend. Legend became myth. And for two and a half thousand years, the ring passed out of all knowledge. Until, when chance came, it ensnared another bearer.
It came to the creature Gollum, who took it deep into the tunnels of the Misty Mountains. And there it consumed him. The ring gave to Gollum unnatural long life. For five hundred years it poisoned his mind, and in the gloom of Gollum's cave, it waited. Darkness crept back into the forests of the world. Rumor grew of a shadow in the East, whispers of a nameless fear, and the Ring of Power perceived its time had come. It abandoned Gollum, but then something happened that the Ring did not intend. It was picked up by the most unlikely creature imaginable: a hobbit, Bilbo Baggins, of the Shire.
For the time will soon come when hobbits will shape the fortunes of all.

Jade sweety is that Gorean ..............runs

 

[jadefirefly]

Is it who what now?


Are you trying to make me do that fucked-up caps thing?

 

[@}-}rebecca----]

Is it who what now?


Are you trying to make me do that fucked-up caps thing?

Different Planet

 

[jadefirefly]

I confused then.


Ooh, ooh, how about this one?
----------

The Babel fish is small, yellow, leechlike, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centers of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish.
Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the NON-existence of God.
The argument goes like this:
`I refuse to prove that I exist,' says God, `for proof denies faith, and without faith I am nothing.'
`But,' says Man, `The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.'
`Oh dear,' says God, `I hadn't thought of that,' and promptly disappears in a puff of logic.
`Oh, that was easy,' says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
Most leading theologians claim that this argument is a load of dingo's kidneys, but that didn't stop Oolon Colluphid making a small fortune when he used it as the central theme of his best-selling book, "Well, That about Wraps It Up for God."
Meanwhile, the poor Babel fish, by effectively removing all barriers to communication between different races and cultures, has caused more and bloodier wars than anything else in the history of creation.

 

[jadefirefly]

Little 'flying circus', perhaps?



Reporter (Eric Idle): Trading was crisp at the start of the day, with some brisk business on the floor. Rubber hardened and string remained confident. Little bits of tin consolidated, although biscuits sank after an early gain and stools remained anonymous. Armpits rallied well after a poor start. Nipples rose dramatically during the morning but had declined by mid afternoon, while teeth clenched and buttocks remained firm. Small dark furry things increased severely on the floor, whilst rude jellies wobbled up and down and bounced against rising thighs which had spread to all parts of the country by mid afternoon. After lunch, naughty things dipped sharply, forcing giblets upwards with the nicky nacky noo. Ting tang tong rankled dithely, little tipples pooped and poppy things went pong. Gibble gabble gobble went the rickety rackety roo...

 

[@}-}rebecca----]

I confused then.


Ooh, ooh, how about this one?
----------

The Babel fish is small, yellow, leechlike, and probably the oddest thing in the Universe. It feeds on brainwave energy received not from its own carrier but from those around it. It absorbs all unconscious mental frequencies from this brainwave energy to nourish itself with. It then excretes into the mind of its carrier a telepathic matrix formed by combining the conscious thought frequencies with nerve signals picked up from the speech centers of the brain which has supplied them. The practical upshot of all this is that if you stick a Babel fish in your ear you can instantly understand anything said to you in any form of language. The speech patterns you actually hear decode the brainwave matrix which has been fed into your mind by your Babel fish.
Now it is such a bizarrely improbable coincidence that anything so mind-bogglingly useful could have evolved purely by chance that some thinkers have chosen to see it as a final and clinching proof of the NON-existence of God.
The argument goes like this:
`I refuse to prove that I exist,' says God, `for proof denies faith, and without faith I am nothing.'
`But,' says Man, `The Babel fish is a dead giveaway, isn't it? It could not have evolved by chance. It proves you exist, and so therefore, by your own arguments, you don't. QED.'
`Oh dear,' says God, `I hadn't thought of that,' and promptly disappears in a puff of logic.
`Oh, that was easy,' says Man, and for an encore goes on to prove that black is white and gets himself killed on the next zebra crossing.
Most leading theologians claim that this argument is a load of dingo's kidneys, but that didn't stop Oolon Colluphid making a small fortune when he used it as the central theme of his best-selling book, "Well, That about Wraps It Up for God."
Meanwhile, the poor Babel fish, by effectively removing all barriers to communication between different races and cultures, has caused more and bloodier wars than anything else in the history of creation.

Sorry no hitchhiking allowed.......runs ( enjoying this )

 

[@}-}rebecca----]

Little 'flying circus', perhaps?



Reporter (Eric Idle): Trading was crisp at the start of the day, with some brisk business on the floor. Rubber hardened and string remained confident. Little bits of tin consolidated, although biscuits sank after an early gain and stools remained anonymous. Armpits rallied well after a poor start. Nipples rose dramatically during the morning but had declined by mid afternoon, while teeth clenched and buttocks remained firm. Small dark furry things increased severely on the floor, whilst rude jellies wobbled up and down and bounced against rising thighs which had spread to all parts of the country by mid afternoon. After lunch, naughty things dipped sharply, forcing giblets upwards with the nicky nacky noo. Ting tang tong rankled dithely, little tipples pooped and poppy things went pong. Gibble gabble gobble went the rickety rackety roo...

We can include it sure though its waaaaaaaaay to easy. Ohhh having a moment of genius brb ......

 

[jadefirefly]

You know, it sucks. There's about a half-dozen movies on that website that have monologues that I just know would kick ass, only they're "only available upon request". That's just so not cool!

 

[@}-}rebecca----]

You know, it sucks. There's about a half-dozen movies on that website that have monologues that I just know would kick ass, only they're "only available upon request". That's just so not cool!

Awww never mind Miss Jade this one I think is just perfect

Physics Colloquiums - Gravitational Entropy (June '98).
Professor Stephen Hawking

The first indication of a connection between black holes and entropy, came in 1970, with my discovery that the area of the horizon of a black hole, always increased. There was an obvious analogy with the Second Law of Thermodynamics, which states that entropy always increases. But it was Jacob Bekenstein, who took the bold step, of suggesting the area actually was the physical entropy, and that it counted the internal states of the black hole. I was very much against this idea at first, because I felt it was a misuse of my horizon area result. If a black hole had a physical entropy, it would also have a physical temperature. If a black hole was in contact with thermal radiation, it would absorb some of the radiation, but it would not give off any radiation, since by definition, a black hole was a region from which nothing could escape. If the thermal radiation was at a lower temperature than the black hole, the loss of entropy down the black hole, would be greater than the increase of horizon area.

This would be a violation of the generalized Second Law, that Bekenstein proposed. With hind sight, this should have suggested that black holes radiate. But no one, including Bekenstein and myself, thought anything could get out of a non rotating black hole. On the other hand, Penrose had shown that energy could be extracted from a rotating black hole, by a classical process. This indicated that there should be a spontaneous emission in the super radiant modes, that would be the quantum counter part of the Penrose process. In trying to understand this emission in the super radiant modes, in terms of quantum field theory in curved spacetime, I stumbled across the fact that even non rotating black holes, would radiate. Moreover, the radiation would be exactly what was required, to prevent a violation of the generalized second law. Bekenstein was right after all, but in a way he hadn’t anticipated. In this talk, I want to discuss the deep reason, for the existence of such gravitational entropy. In my opinion, it is that general relativity, and extensions like supergravity, allow spacetime to have more than one topology. By topology, I mean topology in the Euclidean regime. The topology of a Lorentzian spacetime can change with time, only if there is some pathology, such as a singularity, or closed time like curves. In either of these cases, one would expect the theory to break down.

It was Paul Dirac, my predecessor at Cambridge, who first realized that time evolution in quantum theory, could be formulated as a unitary transformation, generated by the Hamiltonian. This worked well in non relativistic quantum theory, in which the Hamiltonian was just the total energy. It also worked in special relativity, where the Hamiltonian, could be taken to be the time component of the four momentum. But there were problems in general relativity, where neither energy, nor linear momentum, are local quantities. Energy and momentum can only be defined globally, and only for suitable asymptotic behavior.

Dirac himself, developed the Hamiltonian treatment for general relativity. In d dimensions, one can write the metric in the ADM form. That is, one introduces a time coordinate, tau, which I take to be Euclidean, and shift and lapse functions. The Hamiltonian, can then be expressed as an integral, over a surface of constant time. However, the difference from special relativity, was that all the terms in this volume integral, vanished for configurations that satisfied the field equations. I must admit that when I came across the Hamiltonian formulation as a student, I thought, why should one bother working out the volume terms, since they are zero. The answer is, of course, that although the volume terms are zero on solutions, they have non zero Dirac brackets, which become commutators in the quantum theory. Because the volume contributions to the Hamiltonian are zero, its numerical value has to come from surface integrals, at the boundaries of the volume. Such surface terms arise in any gauge theory, including Maxwell theory, when one integrates the constraint equations by parts. In the gravitational case, the Hamiltonian also gets a contribution to the surface term, from the trace K surface term in the action, that is required to cancel the variation in the Einstein Hilbert action, capital R. The surface term in general, makes both the action, and the Hamiltonian, infinite. It is therefore sensible to consider only the difference between the action or Hamiltonian, and those of some reference background solution, that the solutions approach at infinity. This reference background acts as the vacuum, for that sector of the quantum theory. It is normally taken to be flat space, or anti de Sitter space, but I will consider other possibilities.

In asymptotically flat space, if the surfaces of constant tau at infinity, are related by just a time translation, the shift is zero, and the lapse is one. The Hamiltonian surface term at infinity, is then just the mass, plus the electric charge, Q, times the electro static potential, Phi. In a topologically trivial spacetime, one could make the electro static potential zero, by a gauge transformation. However, this will not be possible in non trivial topologies. As I will explain later, magnetic charges do not contribute to the surface term in the Hamiltonian. If the surface of constant tau at infinity, are related by a time translation, plus a rotation through phi, of omega, the surface term at infinity picks up an extra omega J term.

Normally, one considers solutions, which can be foliated by surfaces of constant time, that have boundaries only at infinity, in asymptotically flat space. In such situations, the total Hamiltonian, that is the volume integral, plus the surface terms, will generate unitary transformations, that map the Hilbert space of initial states, into the final ones.

All the quantum states concerned, can be taken to be pure states. There are no mixed states, or gravitational entropy.

However, solutions like black holes, have a Euclidean geometry with non trivial topology. This means that they can’t be foliated by a family of time surfaces, that agree with the usual notion of time. If you try, the family of surfaces will necessarily have intersections, or other singularities, on surfaces of codimension two or more. In fact Euclidean black holes, are the simplest examples. So I will show how the break down of unitary Hamiltonian evolution, gives rise to black hole entropy. I will then go on to more exotic possibilities, like Taub Nut, and Taub bolt. In these cases, the entropy is not necessarily a quarter the area, of a codimension two surface.

As Jim Hartle and I first discovered in 1975, black holes, have a regular Euclidean analytical continuation, if and only if the Euclidean time, tau, is treated like an angular coordinate. It has to be identified with a period, beta, =2 pi over kappa, where kappa is the surface gravity of the horizon. This means that the surfaces of constant tau, all intersect on the horizon, and the concept of a unitary Hamiltonian evolution, will break down there. The surfaces of constant tau, will therefore have an inner boundary at the horizon, and the Hamiltonian will also have contributions from surface terms, at this boundary. If one takes the Hamiltonian vector, to be the combination of the tau and phi Killing vectors that vanishes on the horizon, then the lapse and shift vanish on the horizon. This means that the gravitational part of the surface term, is zero. If the vector potential is also regular on the horizon, the gauge field surface term is also zero.

The thermodynamic partition function, Z, for a system at temperature, beta to the minus one, is the expectation value of e to the minus beta, times the Hamiltonian, summed over all states. As is now well known, this can be represented by a Euclidean path integral, over all fields that are periodic in Euclidean time, with period beta at infinity. Similarly, the partition function for a system with angular velocity, omega, will be given by a path integral over all fields, that are periodic under the combination of a Euclidean time translation, beta, and a rotation, omega beta. One can also specify the gauge potential at infinity. This gives the partition function for a thermodynamic ensemble, with electric and magnetic type charges. The mass, angular momentum, and electric charges of the configurations in the path integral, are not determined by the boundary conditions at infinity. They can be different for different configurations. Each configuration, will therefore be weighted in the partition function, by an e to the minus the charge, times the corresponding potential. On the other hand, the magnetic type charges, are uniquely determined by the boundary conditions at infinity, and are the same for all field configurations in the path integral. The path integral therefore gives the partition function, for a given magnetic charge sector.

The lowest order contribution to the partition function, will be e to the minus I, where I, is the action of the Euclidean black hole solution. The action can be related to the Hamiltonian, as integral H, minus pq dot. In a stationary black hole metric, all the q dots will be zero. Thus the action, I, will be the time period beta, time the value of the Hamiltonian. As I said earlier, the Hamiltonian surface term at infinity, is mass, plus omega J, plus Phi Q, and the Hamiltonian surface term on the horizon, is zero. If one uses the contribution from this action to the partition function, and uses the standard formula, one finds the entropy is zero.

However, because the surfaces of constant Euclidean time, all intersected at the horizon, one had to introduce an inner boundary there. The action, I, = beta times Hamiltonian, is the action for region between the boundary at infinity infinity, and a small tubular neighbourhood of the horizon. But the partition function, is given by a path integral over all metrics with the required behavior at infinity, and no internal boundaries or infinities. One therefore has to add the action of the tubular neighbourhood of the horizon. What ever supergravity theory one is using, and what ever dimension one is in, one can make a conformal transformation of the metric to the Einstein frame, in which the coefficient of the Einstein Hilbert action, capital R, is on over 16 pi G, where G is Newton’s constant in the dimension of the theory. The surface term associate with the Einstein Hilbert action, is one over 8 pi G, times the trace of the second fundamental form. This gives the tubular neighbourhood of the horizon, an action of minus one over 4 G, times the codimension two area of the horizon. If one adds this action to the beta times Hamiltonian, one gets a contribution to the entropy, of area over 4 G, independent of dimension, or of the particular supergravity theory. Higher order curvature terms in the action, would give the tubular neighbourhood an action, that was small compared to area over 4 G, for large black holes. Thus the quarter area law, is universal for black holes. It can be traced to the non trivial topology of Euclidean black holes, which provides an obstruction to foliating them by a family of time surfaces, and using the Hamiltonian to generate a unitary evolution of quantum states. Because the entropy is given by the horizon area in Planck units, one might think that it corresponded to microstates, that are localized near the horizon. However, gravitational entropy, like gravitational energy, can not be localized, but can only be defined globally. This can be seen most clearly in the case of the three dimensional BTZ black hole, to which all four or five dimensional black holes, can be related by a series of U dualities, which preserve the horizon area. The BTZ black hole, is a solution of the 2+1 Einstein equations, with a negative cosmological constant.

Locally, the only solution of these equations, is anti de Sitter space, but the global structure can be different. To see this, one can picture anti de Sitter space, as conformal to the interior of a cylinder in 2+1 Minkowski space. The surface of the cylinder, represents the time like infinity of anti de Sitter space. Similarly, Euclidean anti de Sitter space, is conformal to the interior of a cylinder in three dimensional Euclidean anti de Sitter space. If one now identify this cylinder periodically along its axis, one occasions the background geometry for quantum fields in anti de Sitter space, at a finite temperature. One could identify under the combination of a rotation along the axis and a rotation, but I shall consider only a translation, for simplicity.

The surface of the identified cylinder, representing the boundary at infinity, will be a two torus, with periodically identified tau and phi, as the two coordinates.

However, given a two torus at infinity, there are two topologically distinct ways, that one can fill it in with a two disk, cross a circle. These two ways, are shown as the two anchor rings, or solid tori, on the screen. The circle can be in either the tau or phi directions. The first corresponds to anti de Sitter at a finite temperature, and the second to the BTZ black hole. In the BTZ black, the orbits of the phi Killing vector, do not shrink to zero, because the black hole has no center in the Euclidean region. On the other hand, the orbits of the tau killing vector, shrink to zero at the horizon, which is the center of the disk, cross the circle. One gets a a non zero action and Hamiltonian for the BTZ black hole, by taking the reference background, to be anti de Sitter space at a finite temperature. As before, this leads to an entropy of a quarter the area of the horizon, which in this case, is the length of the phi orbit at the center of the disk. But the BTZ black hole, is completely homogeneous. Thus one can not localize the entropy on the horizon, which is just like the axis in ordinary three dimensional space. It arises from the global mismatch of Euclidean BTZ, with the reference background, which is Euclidean anti de Sitter, periodically identified in the tau direction.

This analysis of the mismatch between the topology of a reference background, and other Euclidean solutions with the same asymptotic behavior, can be extended to other situations. The intersection of surfaces of constant time on the horizon, is only simplest way in which unitary Hamiltonian evolution can break down. Chris Hunter and I, have been investigating more complicated topologies, in which there are other possible singularities in the foliation of spacetime. One might expect that these singularities, would also have entropy associated with them. Since thermal ensembles are periodic in the Euclidean time direction, we considered reference backgrounds, and other Euclidean solutions, which have a U1 isometry group, with Killing vector, K. The isometry group, will have fixed points where K vanishes. Gary Gibbons and I, classified the possible fixed point sets in four dimensions, into two dimensional surfaces we called bolts, and isolated points that we called nuts. However, one can extend this classification scheme, to Euclidean metrics of any dimension. The fixed point sets will then lie on totally geodesic sub manifolds, of even codimension.

Let tau be the parameter of the U1 isometry group. Then the metric can be written in the Kaluza Klein form, with tau as the coordinate on the internal U1. Here V, omega i, and gamma i j, are fields on the d minus one dimensional space, B, of orbits of the isometry group. B would be singular at the fixed points, so one has to leave them out of B, and introduce d minus two dimensional boundaries to B. The coordinate tau can be changed by a Kaluza Klein gauge transformation, that is, by the addition of a function, lambda on B. This changes the one form, omega, by d lambda, but leaves the field strength, F = d omega, unchanged. If the orbit space, B has non trivial homology in dimension two, the two form, F, can have non zero integrals over two cycles in B. In this case the potential one form, omega, will have Dirac like string singularities, on surfaces of dimension d minus three in B. The foliattion of the spacetime by surfaces of constant tau, will break down both at the fixed points of the isometry, and on the Kaluza Klein string singularities of omega, which I will call Misner strings, after Charles Misner who first realized their nature in the Taub nut solution. Misner strings are surfaces of dimension d minus two in the spacetime.

In order to do a Hamiltonian treatment using surfaces of constant tau, one has to cut out small neighbourhoods of the fixed point sets, and of any Misner strings. The action given by beta times the value of the Hamiltonian, will then be the action of the spacetime, with the neighbourhoods removed. Putting back the neighbourhoods, the Einstein Hilbert term will give a contribution of minus a quarter area, for the Misner strings and the d minus two dimensional fixed point sets. But the contribution to the action from lower dimensional fixed points, will be zero. As before, the Hamiltonian surface terms at the fixed points, will be zero, because the lapse and shift vanish there. But the shift won’t vanish on the Misner string, so there will be a Hamiltonian surface term on a Misner string, given by the shift, times a component of the second fundamental form, of the constant tau surfaces. Thus the action will be made up of several contributions. First, there will be beta times the Hamiltonian surface terms at infinity, and on the Misner strings. Then one has to subtract one over 4 G, times the sum of the areas of the bolts, plus the Misner strings. Finally, one has to subtract the same quantities for the reference background. Some or all of these quantities may diverge, but the differences from the reference background will have finite limits, as the boundary is taken to infinity. From now on, I shall mean these finite differences, when I refer to any of these contributions to the action. The partition function, Z, can be related by thermodynamics, to the entropy, and the conserved quantities like energy, angular momentum, and electric charge, whose values are not fixed by the boundary conditions. One has log Z, = the entropy, minus the sum of the conserved quantities, each weighted by its thermodynamic potential. But the Hamiltonian surface term at infinity, multiplied by beta, is by definition, the sum of the conserved quantities, weighted by their thermodynamic potentials. Thus taking the action to be minus log Z, one gets that the entropy is a quarter the area of the bolts, and Misner strings, minus beta times the Hamiltonian surface term on the Misner strings. One can make a Kaluza Klein gauge transformation, by changing tau by a function, lambda, on the orbit space. This will change the position and area of the Misner strings, but the combination, a quarter string area, minus beta the Hamiltonian surface term on the string, will be gauge invariant. Again, this shows that entropy is a global property. It can not be localized in microstates on the Misner string.

The discussion I have given, applies to any gravitational theory in any dimension, which has the Einstein Hilbert action, as the leading term. I shall illustrate it, however, with some examples in four dimensions, that have been worked out by Chris Hunter. Four dimensional metrics, can have several different asymptotic behaviors. In this talk, I shall concentrate on the asymptotically locally flat, and asymptotically locally Euclidean cases, because entropy has not been defined for these spaces previously.

Asymptotically local flat solutions, have a Nut charge, or magnetic type mass, N, as well as the ordinary electric type mass, M. The Nut charge is beta over 8 pi, times the first Chern number of the U1 bundle, over the sphere at infinity, in the orbit space, B. The natural reference backgrounds for solutions with Nut charge, are the self dual multi Taub Nut solutions, which have M=N. When written in Kaluza Klein form, the multi Taub Nut solutions what no bolts, or fixed point sets of dimension two. They do however, have a number of Nuts, or fixed point sets of dimension zero. From each Nut, there is a Misner string, leading to either another Nut, or infinity. The positions and areas of the Misner strings, are gauge dependent. However, a quarter the area of the Misner strings, minus beta times the Hamiltonian surface term on the strings, is gauge invariant, and is independent of the position of the Nuts in the three dimensional flat orbit space. Thus the entropy of the multi Taub Nuts, is zero, as one would expect, since they define the vacuum for that sector of the theory.

There are, however, asymptotically locally flat solutions, that are not multi Taub Nut. The prime example, is the so called Taub bolt solution, discovered by Don page. As its name suggests, this solution has a bolt, with area 12 pi N squared. It also has a Misner string, stretching from the bolt to infinity. The Chern number at infinity, is one. Thus the appropriate reference background, is the single self dual Taub Nut. When one calculates the entropy according to the prescription I have given, the result is, pi N squared. Note that this is not a quarter the area of the bolt, which would have given 3 pi N squared. The difference comes from the different Misner string area and Hamiltonian contributions, in Taub Nut and Taub bolt.

In the asymptotically locally Euclidean case, the appropriate reference backgrounds, are the orbifolds obtained by identifying Euclidean flat space, under a discrete sub group, Gamma, of SU2, that acts freely on the three sphere. The ALE self dual instantons, have these boundary conditions. They can be written in Kaluza Klein form, with bolts, nuts, and Misner strings. The reference backgrounds, can also be written in Kaluza Klein form, with a nut at the orbifold point, and a Misner string from the orbifold point, to infinity. However, the entropy, calculated according to the prescription I have given, turns out to be zero. This is what one would expect, because the ALE instantons, have the same super symmetry as the reference backgrounds. It is only when one has solutions with less super symmetry than the background, that one gets entropy. Examples are non extreme black holes, which have no super symmetry, or extreme black holes with central charges, which have reduced super symmetry.

One can show that there are no vacuum ALE metrics, with less super symmetry than the reference background. The Israel Wilson family of Einstein Maxwell solutions, however, contains non self dual ALE, and even asymptotically Euclidean solutions, with an asymptotically constant self dual Maxwell field at infinity. Since these solutions are not super symmetric, and have different topology to the reference background, one would expect them to have entropy, and this is confirmed by calculation of examples.

One might think instantons with a self dual Maxwell field at infinity, were not physically relevant. However, one can promote them to being Einstein Yang Mills solutions, with a constant self dual Yang Mills field at infinity. One could then match them to Yang Mills instantons in flat space, with large winding numbers, which can have regions where the Yang Mills field, is almost constant.

Finally, to show that the expression we propose for the entropy, can be applied in more than four dimensions, consider the five sphere, of radius, R. This can be regarded as a solution of a five dimensional theory, with cosmological constant. One can take the U1 isometry group, to have a fixed point set on a three sphere of radius R. In this case there are no Misner strings. So the formula gives an entropy of, pi squared, R cubed, over 2G. However, one can choose a different U1 isometry, whose orbits are the Hopf fibration of the five sphere. This isometry group, has no fixed points. So the usual connection between entropy, and the fixed points, does not apply. But the orbit space of the Hopf fibration, is CP2. The Kaluza Klein two form, F, is the harmonic two form on CP2. The one form potential, omega, for this has a Dirac string on a two surface in the orbit space. When promoted to the full spacetime, this becomes a three dimensional Misner string. The area of the Misner string divided by 4G, minus beta times the Hamiltonian surface term on the Misner string, is again the entropy, pi squared R cubed, over 2G. This example is fairly trivial, but it shows that the method can be extended to higher dimensions.

I think there are three morals can be drawn from this work.

The first is that gravitational entropy just depends on the Einstein Hilbert action. It doesn’t require super symmetry, string theory, or p-branes.

The second is that entropy is a global quantity, like energy or angular momentum, and shouldn’t be localized on the horizon. The various attempts to identify the microstates responsible for black hole entropy, are in fact constructions of dual theories, that live in separate spacetimes.

The third moral, is that entropy arises from a failure to foliate the Euclidean regime, with a family of time surfaces. This would suggest that there would not be a unitary S matrix, for particle scattering described by a Euclidean section, with non trivial topology. No particle scattering situation, with non trivial Euclidean topology, has definitely been shown to exist, but the asymptotically Euclidean solutions with a constant Maxwell field at infinity, are very suggestive. They would seem to point to loss of quantum coherence and information, in black holes. This is the major unresolved question, in the quantum theory of black holes. Let’s hope this meeting, gives us new insights into the problems.

 

[jadefirefly]

Have I mentioned lately that you are a very, very cruel woman? That hurts my brain..

 

[Salvor-Hardon]

Nice shades Salvor........ohh now please keep in mind I am an Australian so while I get the 'Oscar Meyer Wiener' reference ( we call them footy franks....ick) I am wondering is there a special dance that goes with it (I'm a little teapot style sort of thing) ........that we could encourage Miss Jade to also learn as her finale ...smiles.

Patiently awaiting your reply

@}-}rebecca-----

Thank you, I have recently discovered that the fuzzy nose and glasses combo drives women wild. I put them on and spontaneous orgasms erupt in a 10 foot radius.

To the best of my knowledge there is no dance that goes with the "Oscar Meyer Weiner" song, however performing it naked always makes for an entertaining evening

 

[jadefirefly]

And besides, I already know the Oscar Mayer weiner song. And the bologna song, too.



(Don't ask. Sometimes I sing them when I'm bored. )

 

[shy slave]

Glad you like that one from Macbeath Babies

Macbeath is my favourite Shakespeare play and thats one of my favourite speeches. I know many who quote Lady M's 'Out damned spot' but what good is a woman gone mad because of her own wickedness, much better to enjoy being what you really are and reveal in it

Rebecca!!!! That Stephen Hawking piece is just damned mean!!!
I only managed to get through the first half dozen lines before my head almost exploded. Have you considered you may be a closet Domme???

Jade if this heads down the Flying Circus Eric Idle route, its only a matter of time before the Dead Parrot Sketch from Monty Python is quoted.
I saw a comment years ago that said if you have 5 men in a room between three of them, they will be able to quote that sketch. Have often found it to be true

 

[@}-}rebecca----]

Have I mentioned lately that you are a very, very cruel woman? That hurts my brain..

Ohhhh........good Morning to you as well Miss Jade.......smiles............hmmmn and yesterday let me see what was it ......"I, of course, bow to miss Rebecca's supreme wisdom. "............yes.......yes thats it ......winksmiles

 

[@}-}rebecca----]

Thank you, I have recently discovered that the fuzzy nose and glasses combo drives women wild. I put them on and spontaneous orgasms erupt in a 10 foot radius.

To the best of my knowledge there is no dance that goes with the "Oscar Meyer Weiner" song, however performing it naked always makes for an entertaining evening

Ohh goodness Salvor........now there is some imagery you may have warned me about sans caffeine this morning.......livin Da Vida Loca ........oh chite...... I think am channeling Carmen Miranda in pajamas now.......no dance huh.......sniff