Effectiveness of one-dimensional gas models for black holes

Ghosh, Amit

doi:10.1016/s0370-2693(98)00268-8

Cited by 4 publications

(5 citation statements)

References 17 publications

(32 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since, in our case ξ ∼ s −1 near the critical point, we obtain R (R) ∼ ξ 1 . Therefore, we can again conclude that the effective spatial dimension d = 1 for any extremal black hole, which is in agreement with the claim of the recent papers [57,58]. Thus, from the thermogeometric approach, we can again generally prove that the effective spatial dimension of an extremal black hole is one.…”

Section: The Ruppeiner Metricsupporting

confidence: 91%

General framework to study the extremal phase transition of black holes

et al. 2019

View full text Add to dashboard Cite

We investigate the universality of some features for the extremal phase transition of black holes and unify all the approaches which have been applied in different spacetimes. Unlike the other existing approaches where the information of the spacetime and its dimension is directly used to get various results, we provide a general formulation in which those results are obtained for any arbitrary black hole spacetime having an extremal limit. Calculating the second order moments of fluctuations of some thermodynamic quantities we show that, the phase transition occurs only in the microcanonical ensemble. Without considering any specific black hole we calculate the values of critical exponents for this type of phase transition. These are shown to be in agreement with the values obtained earlier for metric specified cases. Finally we extend our analysis to the geometrothermodynamics (henceforth GTD) formulation. We show that for any black hole, if there is an extremal point, the Ricci scalar for the Ruppeiner metric must diverge at that point.

show abstract

Section: The Ruppeiner Metricsupporting

confidence: 91%

General framework to study the extremal phase transition of black holes

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Now we come back to the subtle point we mentioned above: the signature flip of the curvature. As is said before, Ghosh recently found [14] the relation between the near extremal BTZ black hole and (1+1)-dimensional conformal field theory via the ideal bosonic gas model in one dimension. This strongly imples that the system is composed of bosons.…”

Section: Discussionmentioning

confidence: 66%

“…This signature difference looks strange, on which we will dicuss in the later section. Here it should also be mentioned that more recently Ghosh [14] has constructed a one-dimensional Boson gas model to provide the correct expression for entropies for extremal and near-extremal BTZ black holes. Therefore our result is consistent with the one-dimensional gas model of the near extremal BTZ black hole.…”

Section: Thermodynamic Curvaturementioning

confidence: 99%

See 1 more Smart Citation

Thermodynamic curvature of the BTZ black hole

1999

View full text Add to dashboard Cite

In this paper we apply the concept of thermodynamic geometry to the Bañados-Teitelboim-Zanelli ͑BTZ͒ black hole. We find the thermodynamic curvature diverges at the extremal limit of the black hole, which means the extremal black hole is the critical point with the temperature zero. We also study the effective dimensionality of the underlying statistical model. Near the critical point, the picture is clear; the spatial dimension of the underlying statistical model is just one, which agrees with other results. However, far from the critical point, the dimension becomes less than one and even negative. In order to interpret this result, we resort to a qualitative analogy with the Takahashi gas model. ͓S0556-2821͑99͒04516-6͔ PACS number͑s͒: 04.70.Dy, 04.60. Kz, 05.70.Jk Over the decades the statistical interpretation of blackhole entropy has been one of the most fascinating subjects. There have been many approaches to the problem, although nothing was completely successful. One curiosity about black-hole thermodynamics is that it looks different from an ordinary thermodynamical system, due to the negative heat capacity. This makes it hard to compose its thermodynamic ensemble and to make the underlying statistical model. One way to study the statistical aspects is to assume the microcanonical ensemble for an isolated black hole. Actually, in this way one can understand the critical behavior for the near extremal black hole. The critical exponents satisfying the scaling law even tells us the dimensionality of the underlying statistical model.In this paper, we suggest another tool useful for studying the statistical properties including the fluctuation, the critical behavior, and so on. This is the thermodynamic geometry. It defines a metric on the space of thermodynamic variables. ͑Of course, it has nothing to do with the geometry of space and time.͒ Here, the thermodynamic potential becomes the geometrical potential generating the metric components. The thermodynamic variables constitute the coordinates for the geometry. Details will be given below through the example of the Bañados-Teitelboim-Zanelli ͑BTZ͒ black hole ͓2͔. As is known, the BTZ black hole could play an important role in understanding entropy and some dynamical properties of certain five-and four-dimensional black holes in supergravity theories, because of the U duality between the BTZ black hole and those high-dimensional black holes ͓3͔. For a review see ͓4͔.In general, it is technically difficult to define the zerotemperature critical point, as is the case with the black hole. Conventional definition for the zero-temperature critical point is the point where at least one of the second derivatives of some thermodynamic potential diverges ͓1͔. However, in the language of thermodynamic geometry one can define it unambiguously as the point where the thermodynamic curvature ͑the curvature with respect to the thermodynamic metric͒ diverges. This is based on the fact that thermodynamic curvature is proportional to the correlation volume ͓5͔:where 2 is ...

show abstract

“…Thus, to describe the thermodynamics of these black holes, one substitutes d = 3 in (51). This gives a (1 + 1)-dimensional gas, which is known to reproduce the entropy and Hawking radiation rates of near-extremal black holes in string theory [38][39][40]. Some other thermodynamic properties of BTZ black holes have also been shown to follow from an effective one-dimensional gas [41].…”

Section: Matching Thermodynamicsmentioning

confidence: 91%

Anti-de Sitter black holes, perfect fluids and holography

Das¹,

Husain²

2003

Class. Quantum Grav.

View full text Add to dashboard Cite

We consider asymptotically anti-de Sitter black holes in d-spacetime dimensions in the thermodynamically stable regime. We show that the Bekenstein-Hawking entropy and its leading order corrections due to thermal fluctuations are reproduced by a weakly interacting fluid of bosons and fermions ('dual gas') in ∆ = α(d − 2) + 1 spacetime dimensions, where the energy-momentum dispersion relation for the constituents of the fluid is assumed to be ǫ = κp α . We examine implications of this result for entropy bounds and the holographic hypothesis.

show abstract

Effectiveness of one-dimensional gas models for black holes

Abstract: A one-dimensional gas model has been constructed and is shown to provide correct expressions for entropies for extremal and near-extremal BTZ black holes. Recently suggested boosting of black strings is also used to compute the entropy for the Schwarzschild black hole from this gas model.

Cited by 4 publications

References 17 publications

General framework to study the extremal phase transition of black holes

General framework to study the extremal phase transition of black holes

Thermodynamic curvature of the BTZ black hole

Anti-de Sitter black holes, perfect fluids and holography

Contact Info

Product

Resources

About