String theory calculation of Extremal black hole entropy problem

  • #1
TL;DR Summary
more recent papers of Extremal black hole entropy
one of the claimed successes of string theory is its ability to derive the correct Hawking-Bekenstein equations to calculate the quantum entropy of a black hole without any free paramenters, specifically Extremal black hole entropy using supersymmetry and maximal charge.

I was wondering if string theory use of D-branes can also reproduce correct Hawking radiation but I understand extremel black holes do not emit Hawking radiation.

there are at least 2 papers I know of,

Extremal limits and black hole entropy​

Sean M. Carroll, Matthew C. Johnson, Lisa Randall

Taking the extremal limit of a non-extremal Reissner-Nordström black hole (by externally varying the mass or charge), the region between the inner and outer event horizons experiences an interesting fate -- while this region is absent in the extremal case, it does not disappear in the extremal limit but rather approaches a patch of AdS2×S2. In other words, the approach to extremality is not continuous, as the non-extremal Reissner-Nordström solution splits into two spacetimes at extremality: an extremal black hole and a disconnected AdS space. We suggest that the unusual nature of this limit may help in understanding the entropy of extremal black holes.


Extremal black holes, gravitational entropy and nonstationary metric fields​

Ariel Edery, Benjamin Constantineau

We show that extremal black holes have zero entropy by pointing out a simple fact: they are time-independent throughout the spacetime and correspond to a single classical microstate. We show that non-extremal black holes, including the Schwarzschild black hole, contain a region hidden behind the event horizon where all their Killing vectors are spacelike. This region is nonstationary and the time t labels a continuous set of classical microstates, the phase space [hab(t),Pab(t)], where hab is a three-metric induced on a spacelike hypersurface Σt and Pab is its momentum conjugate. We determine explicitly the phase space in the interior region of the Schwarzschild black hole. We identify its entropy as a measure of an outside observer's ignorance of the classical microstates in the interior since the parameter t which labels the states lies anywhere between 0 and 2M. We provide numerical evidence from recent simulations of gravitational collapse in isotropic coordinates that the entropy of the Schwarzschild black hole stems from the region inside and near the event horizon where the metric fields are nonstationary; the rest of the spacetime, which is static, makes no contribution. Extremal black holes have an event horizon but in contrast to non-extremal black holes, their extended spacetimes do not possesses a bifurcate Killing horizon. This is consistent with the fact that extremal black holes are time-independent and therefore have no distinct time-reverse.

" We show that extremal black holes have zero entropy"

If these papers are correct, then using QFT the actual entropy of an extremel black hole is 0, zero.

string theory greatest theoretical triump h in quantum gravity is to use D-branes to caculate extremel black hole entropy and arrive at the Hawking-Bekenstein equations without any free parameters.

but if the papers above are correct, the actual value of extremel black hole entropy is 0 and not Hawking-Bekenstein equations .

does this imply that sting theory incorrect formula for extremel black holes, extremel black hole entropy is not Hawking-Bekenstein equations but simply zero.

should the correct theory of quantum gravity, which apparently is not string theory, calculate from first principles that extremel black hole entropy is not Hawking-Bekenstein equations but simply zero.

Answers and Replies

  • #2
another paper

Geometric aspects of Extremal Kerr black hole entropy​

E M Howard

Extreme Black holes are an important theoretical laboratory for exploring the nature of entropy. We suggest that this unusual nature of the extremal limit could explain the entropy of extremal Kerr black holes. The time-independence of the extremal black hole, the zero surface gravity, the zero entropy and the absence of a bifurcate Killing horizon are all related properties that define and reduce to one single unique feature of the extremal Kerr spacetime. We suggest the presence of a true geometric discontinuity as the underlying cause of a vanishing entropy.

Comments:10 pages, published in Journal of Modern Physics, 2013, 4, 357-363. arXiv admin note: text overlap with arXiv:hep-th/9608162, arXiv:1201.4017 by other authors

"The time-independence of the extremal black hole, the zero surface gravity, the zero entropy"
  • #3

Lectures on Strings and Dualities​

Cumrun Vafa

In this set of lectures I review recent developments in string theory emphasizing their non-perturbative aspects and their recently discovered duality symmetries. The goal of the lectures is to make the recent exciting developments in string theory accessible to those with no previous background in string theory who wish to join the research effort in this area. Topics covered include a brief review of string theory, its compactifications, solitons and D-branes, black hole entropy and web of string dualities. (Lectures presented at ICTP summer school, June 1996)

Comments:53 pages
Subjects: High Energy Physics - Theory (hep-th)
Report number:HUTP-97/A009
Cite as:arXiv:hep-th/9702201
(or arXiv:hep-th/9702201v1 for this version)
  • #4

Microscopic Origin of the Bekenstein-Hawking Entropy​

A. Strominger, C. Vafa

The Bekenstein-Hawking area-entropy relation SBH=A/4 is derived for a class of five-dimensional extremal black holes in string theory by counting the degeneracy of BPS soliton bound states.

Comments:12 pages. Relatively minor corrections and additions to discussion
Subjects: High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc)
Report number:HUTP-96/A002, RU-96-01
Cite as:arXiv:hep-th/9601029

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