Scaling laws at the critical point on black hole equilibrium series

We investigate the evolution of a scalar field propagating in Reissner-Nordström Anti-de Sitter spacetime. Due to the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object-picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.

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“…It has been shown that there is a second order phase transition in the extreme limit of black holes [28,29,30].…”

Section: Quasinormal Modes For Highly Charged Ads Black Holementioning

confidence: 99%

Evolution of a massless scalar field in Reissner-Nordström anti–de Sitter spacetimes

2001

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“…[11] and references therein). However, the interpretation of the divergences in the specific heats and generalized susceptibilities (in particular, their interpretation as a true phase transition and their relation to the stability of the system) is not clear and has been subject of debate [12,13,14,15,16,17,18]. In a String Theory context some partial attempts to relate dynamical stability and local thermodynamical stability have been put forward as well [19], but currently the present status of this subject is not clear [20] (see also the third reference listed in [4]).…”

Section: Introductionmentioning

confidence: 99%

Stability and critical phenomena of black holes and black rings

2005

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We revisit the general topic of thermodynamical stability and critical phenomena in black hole physics, analyzing in detail the phase diagram of the five dimensional rotating black hole and the black rings discovered by Emparan and Reall. First we address the issue of microcanonical stability of these spacetimes and its relation to thermodynamics by using the so-called Poincaré (or "turning point") method, which we review in detail. We are able to prove that one of the black ring branches is always locally unstable, showing that there is a change of stability at the point where the two black ring branches meet. Next we study divergence of fluctuations, the geometry of the thermodynamic state space (Ruppeiner geometry) and compute the appropriate critical exponents and verify the scaling laws familiar from RG theory in statistical mechanics. We find that, at extremality, the behaviour of the system is formally very similar to a second order phase transition.

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“…In order to discuss the critical behavior of the isolated black p-branes as in [18,19], it is appropriate to choose the microcanonical ensemble. Here the proper Massieu function is given by the entropy of black p-branes.…”

Section: Scaling Laws and Critical Exponentsmentioning

confidence: 99%

“…He found that the extremal Kerr-Newman black hole has a critical point and some critical exponents also obey the scaling laws [18].…”

Section: Introductionmentioning

confidence: 99%

Critical behavior for the dilaton black holes

Cai

Myung

1997

Nuclear Physics B

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We study the critical behavior in the black p-branes and four dimensional charged dilaton black holes. We calculate the thermodynamic fluctuations in the various (microcanonical, canonical, and grandcanonical) ensembles. It is found that the extremal limit of some black configurations has a critical point and a phase transition takes place from the extremal to nonextremal black configurations. Some critical exponents are obtained, which satisfy the scaling laws. This is related to the fact that the entropy of these black configurations is a homogeneous function.

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Scaling laws at the critical point on black hole equilibrium series

Cited by 25 publications

References 29 publications

Evolution of a massless scalar field in Reissner-Nordström anti–de Sitter spacetimes

Evolution of a massless scalar field in Reissner-Nordström anti–de Sitter spacetimes

Stability and critical phenomena of black holes and black rings

Critical behavior for the dilaton black holes

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