Black Hole Entropy in Quantum Gravity

[marcus]

A good place to begin might be with Enrique Alvarez recent survey "Loops versus Strings" given in July to an audience of HEP people at the Portoroz conference "What comes beyond the standard model?"

http://arxiv.org/gr-qc/0307090

Alvarez is a recognized string theorist who has published some 16 articles since 1997 IIRC. He is at U. Madrid, very likely was the thesis advisor for someone name Marchesano now at Madison doing string postdoc. Dont know but a likely guess. Lethe knows Marchesano. Anyway Alvarez was asked to give a survey on Loops versus Strings and his viewpoint is not that of a relativist (a GR expert) but of a string-brane person.

But he is not necessarily propagandizing, as string-folk sometimes do when they feel threatened and are talking to outsiders. He seems to me to be being fair and objective according to his own lights. This is July 2003.

Page 10:

"4.2 Big Results [of string theory]

Perhaps the main result is that graviton physics in flat space is well defined for the first time, and this is no minor accomplishment...

The other Big Result[ref to Strominger/Vafa] is that one can correctly count states of extremal black holes as a function of charges. This is at the same time astonishing and disappointing. It clearly depends strongly on the objects being BPS states (that is, on supersymmetry), and the result has not been extended to non-supersymmetric configurations. On the other hand, as we have said, it exactly reproduces the entropy as a function of a sometimes large number of charges, without any adjustable parameter..."

My reaction is that dependence on supersymmetry, which is far from being established, is disconcerting as is the restriction to extremal (and, I understand, near-extremal) holes. These are exotic objects which unlike the black holes one sees evidence of in nature are electrically charged to the max. An extremal hole is as electrically charged as it can possibly be and continue to exist.
It would be more reassuring if there were a stringy result for Schwartzschild holes----the ordinary vanilla electrically neutral hole we are used to thinking about.

However the Loop result which was gotten the same year as the
Strominger/Vafa one (1996) and applies to Schwarzschild holes, has an undetermined parameter called the Immirzi parameter!
So the Loop derivation of the same entropy formula is also unsatisfactory. This fly in the ointment has, in turn, generated further theoretical investigation (work by Corichi, Swain etc) and it may be that some new insights will come out of it.

But the most dubious thing about the String-Brane version of the entropy formula is something Alvarez did not even elude to. However another String Theorist, Gary Horowitz of UCSB, did, at the Ninth Marcel Grossman Meeting at Rome July 2000, in his talk
"Quantum Gravity at the Turn of the Millennium".

http://arxiv.org/gr-qc/0011089

[If you catch a string theorist being honest and talking to his peers, he is apt to say similar things to Lee Smolin---but some people choose to discount Smolin as biased! Smolin's words on this particular matter strike me as, if anything, more indulgent and congratulatory to string than those of Horowitz the insider, speaking on the level]

Horowitz on page 12:

"Both string theory and quantum geometry [by this he means LQG: the attempt to quantize spacetime geometry, i.e. GR] have given strong evidence that...They can reproduce the entropy of black holes by counting quantum states. But they do so in very different ways. Quantum geometry is directly counting fluctuations of the event horizon, while string theory extrapolates the black hole to weak coupling and counts states of strings (and branes) in flat spacetime. At the moment, the string calculations give exact results...only for extreme and near extreme charged black holes..."

well, I need to go, but will get back to this later on

 

[jeff]

Originally posted by marcus
...one can correctly count states of extremal black holes as a function of charges. This is at the same time astonishing and disappointing. It clearly depends strongly on the objects being BPS states (that is, on supersymmetry), and the result has not been extended to non-supersymmetric configurations. On the other hand, as we have said, it exactly reproduces the entropy as a function of a sometimes large number of charges, without any adjustable parameter..."

However the Loop result which was gotten the same year as the Strominger/Vafa one (1996) and applies to Schwarzschild holes, has an undetermined parameter called the Immirzi parameter!So the Loop derivation of the same entropy formula is also unsatisfactory.

"Both string theory and quantum geometry [by this he means LQG: the attempt to quantize spacetime geometry, i.e. GR] have given strong evidence that...They can reproduce the entropy of black holes by counting quantum states. But they do so in very different ways. Quantum geometry is directly counting fluctuations of the event horizon, while string theory extrapolates the black hole to weak coupling and counts states of strings (and branes) in flat spacetime. At the moment, the string calculations give exact results...only for extreme and near extreme charged black holes..."

You are wrongly equating the short-comings of the LQG and SMT results. To explain,

The black hole entropy formula was initially derived thermodynamically, but Strominger and Vafa showed that states of the very large class of supersymmetric holes can be correctly counted in the kind of precise and controlled way we'd expect to exist if the relation between thermodynamics and statistical mechanics is the same for extremal black holes as it is for more prosaic systems. Thus it's perfectly natural to expect - indeed there's no reason not to - that SMT will be shown to produce the correct formula for any black hole.

On the other hand, the problem is far more serious in the case of LQG because right out of the box there's an ambiguity in the black hole entropy formula it produces and no apparent additional or unexplored structure in LQG from which a resolution might spring. In fact, it's the kind of ambiguity that often signals some underlying inconsistency in a theory. Let me give a couple of examples of this. One is that semiclassical euclidean quantum gravity predicted wormholes without being able to specify where below the Planck scale they'd appear. Another is gell-mann's and hartle's decohering histories approach to applying quantum theory to the entire universe which predicts the existence of "quasiclassical" domains without being able to specify the conditions under which they occur. Interest in both these approaches waned as much - perhaps more than - for the occurrence of these ambiguities as for anything else.

Originally posted by marcus
My reaction is that dependence on supersymmetry, which is far from being established, is disconcerting as is the restriction to extremal (and, I understand, near-extremal) holes. These are exotic objects which unlike the black holes one sees evidence of in nature are electrically charged to the max. An extremal hole is as electrically charged as it can possibly be and continue to exist.

Just so there's no confusion among readers, supersymmetry and extremality aren't independent concepts: Extremal holes are supersymmetric.

As far as the efficacy of supersymmetrizing theories is concerned, the trend in physics has been towards the enlargement and merging of symmetries, the idea of which is to bring different families of particles together to interact under one force (as in the case of electro-weak interactions), and there's every reason to expect this trend to continue. But without supersymmetry, there's no way to unify the two basic types of elementary objects, namely bosons and fermions, and it's for this reason that theorists are betting that the superpartners of the known particles will show up. Not surprisingly, attempts are being made to supersymmetrize LQG as well.

Originally posted by marcus
It would be more reassuring if there were a stringy result for Schwartzschild holes

That's for sure.

Originally posted by marcus
not necessarily propagandizing, as string-folk sometimes do when they feel threatened and are talking to outsiders.

This is like claiming that capitalists these days feel threatened by communists.

 

[R0man]

.

My reaction is that the String-Brane "exact" results are not really exact, since they are restricted to extremal and near-extremal holes. This is a limitation that needs to be addressed and resolved. Additionally, the reliance on supersymmetry is a concern, as it is not yet established and may not hold in reality. The Loop result, while applicable to Schwarzschild holes, also has its own limitations and an undetermined parameter. The fact that both approaches give the same result, but in different ways, is intriguing and may lead to further insights. However, the discrepancy between the two approaches and the limitations of both results highlight the need for more research and investigation in this area.