1,701 research outputs found
State-space Correlations and Stabilities
The state-space pair correlation functions and notion of stability of
extremal and non-extremal black holes in string theory and M-theory are
considered from the viewpoints of thermodynamic Ruppeiner geometry. From the
perspective of intrinsic Riemannian geometry, the stability properties of these
black branes are divulged from the positivity of principle minors of the
space-state metric tensor. We have explicitly analyzed the state-space
configurations for (i) the two and three charge extremal black holes, (ii) the
four and six charge non-extremal black branes, which both arise from the string
theory solutions. An extension is considered for the ---
multi-centered black branes, fractional small black branes and two charge
rotating fuzzy rings in the setup of Mathur's fuzzball configurations. The
state-space pair correlations and nature of stabilities have been investigated
for three charged bubbling black brane foams, and thereby the M-theory
solutions are brought into the present consideration. In the case of extremal
black brane configurations, we have pointed out that the ratio of diagonal
space-state correlations varies as inverse square of the chosen parameters,
while the off diagonal components vary as inverse of the chosen parameters. We
discuss the significance of this observation for the non-extremal black brane
configurations, and find similar conclusion that the state-space correlations
extenuate as the chosen parameters are increased.Comment: 35 pages, Keywords: Black Hole Physics, Higher-dimensional Black
Branes, State-space Correlations and Statistical Configurations. PACS
numbers: 04.70.-s Physics of black holes; 04.70.Bw Classical black holes;
04.70.Dy Quantum aspects of black holes, evaporation, thermodynamics;
04.50.Gh Higher-dimensional black holes, black strings, and related object
State-space Manifold and Rotating Black Holes
We study a class of fluctuating higher dimensional black hole configurations
obtained in string theory/ -theory compactifications. We explore the
intrinsic Riemannian geometric nature of Gaussian fluctuations arising from the
Hessian of the coarse graining entropy, defined over an ensemble of brane
microstates. It has been shown that the state-space geometry spanned by the set
of invariant parameters is non-degenerate, regular and has a negative scalar
curvature for the rotating Myers-Perry black holes, Kaluza-Klein black holes,
supersymmetric black holes, - configurations and the
associated BMPV black holes. Interestingly, these solutions demonstrate that
the principal components of the state-space metric tensor admit a positive
definite form, while the off diagonal components do not. Furthermore, the ratio
of diagonal components weakens relatively faster than the off diagonal
components, and thus they swiftly come into an equilibrium statistical
configuration. Novel aspects of the scaling property suggest that the
brane-brane statistical pair correlation functions divulge an asymmetric
nature, in comparison with the others. This approach indicates that all above
configurations are effectively attractive and stable, on an arbitrary
hyper-surface of the state-space manifolds. It is nevertheless noticed that
there exists an intriguing relationship between non-ideal inter-brane
statistical interactions and phase transitions. The ramifications thus
described are consistent with the existing picture of the microscopic CFTs. We
conclude with an extended discussion of the implications of this work for the
physics of black holes in string theory.Comment: 44 pages, Keywords: Rotating Black Holes; State-space Geometry;
Statistical Configurations, String Theory, M-Theory. PACS numbers: 04.70.-s
Physics of black holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum
aspects of black holes, evaporation, thermodynamics; 04.50.Gh
Higher-dimensional black holes, black strings, and related objects. Edited
the bibliograph
Black Strings, Black Rings and State-space Manifold
State-space geometry is considered, for diverse three and four parameter
non-spherical horizon rotating black brane configurations, in string theory and
-theory. We have explicitly examined the case of unit Kaluza-Klein momentum
black strings, circular strings, small black rings and black
supertubes. An investigation of the state-space pair correlation functions
shows that there exist two classes of brane statistical configurations, {\it
viz.}, the first category divulges a degenerate intrinsic equilibrium basis,
while the second yields a non-degenerate, curved, intrinsic Riemannian
geometry. Specifically, the solutions with finitely many branes expose that the
two charged rotating black strings and three charged rotating small
black rings consort real degenerate state-space manifolds. Interestingly,
arbitrary valued -dipole charged rotating circular strings and Maldacena
Strominger Witten black rings exhibit non-degenerate, positively curved,
comprehensively regular state-space configurations. Furthermore, the
state-space geometry of single bubbled rings admits a well-defined, positive
definite, everywhere regular and curved intrinsic Riemannian manifold; except
for the two finite values of conserved electric charge. We also discuss the
implication and potential significance of this work for the physics of black
holes in string theory.Comment: 41 pages, Keywords: Rotating Black Branes; Microscopic
Configurations; State-space Geometry, PACS numbers: 04.70.-s Physics of black
holes; 04.70.Bw Classical black holes; 04.70.Dy Quantum aspects of black
holes, evaporation, thermodynamic
State-space Geometry, Statistical Fluctuations and Black Holes in String Theory
We study the state-space geometry of various extremal and nonextremal black
holes in string theory. From the notion of the intrinsic geometry, we offer a
new perspective of black hole vacuum fluctuations. For a given black hole
entropy, we explicate the intrinsic state-space geometric meaning of the
statistical fluctuations, local and global stability conditions and long range
statistical correlations. We provide a set of physical motivations pertaining
to the extremal and nonextremal black holes, \textit{viz.}, the meaning of the
chemical geometry and physics of correlation. We illustrate the state-space
configurations for general charge extremal black holes. In sequel, we extend
our analysis for various possible charge and anticharge nonextremal black
holes. From the perspective of statistical fluctuation theory, we offer general
remarks, future directions and open issues towards the intrinsic geometric
understanding of the vacuum fluctuations and black holes in string theory.
Keywords: Intrinsic Geometry; String Theory; Physics of black holes;
Classical black holes; Quantum aspects of black holes, evaporation,
thermodynamics; Higher-dimensional black holes, black strings, and related
objects; Statistical Fluctuation; Flow Instability.
PACS: 02.40.Ky; 11.25.-w; 04.70.-s; 04.70.Bw; 04.70.Dy; 04.50.Gh; 5.40.-a;
47.29.KyComment: 28 pages. arXiv admin note: substantial text overlap with
arXiv:1102.239
Can the correlated stability conjecture be saved?
Correlated stability conjecture (CSC) proposed by Gubser and Mitra [1,2]
linked the thermodynamic and classical (in)stabilities of black branes. In [3]
it was shown that the thermodynamic instabilities, specifically the negative
specific heat, indeed result in the instabilities in the hydrodynamic spectrum
of holographically dual plasma excitations. Counter-examples of CSC were
presented in the context of black branes with scalar hair undergoing a
second-order phase transition [4,5]. The latter translationary invariant
horizons have scalar hair, raising the question whether the asymptotic
parameters of the scalar hair can be appropriately interpreted as additional
charges leading to a generalization of the thermodynamic stability criterion.
In this paper we show that the generalization of the thermodynamic stability
criterion of this type can not save CSC. We further present a simple
statistical model which makes it clear that thermodynamic and dynamical
(in)stabilities generically are not correlated.Comment: 9 pages, 2 figures; v2: JHEP versio
Thermodynamic Geometry and Phase Transitions of AdS Braneworld Black Holes
The thermodynamics and phase transitions of charged RN-AdS and rotating
Kerr-AdS black holes in a generalized Randall-Sundrum braneworld are
investigated in the framework of thermodynamic geometry. A detailed analysis of
the thermodynamics, stability and phase structures in the canonical and the
grand canonical ensembles for these AdS braneworld black holes are described.
The thermodynamic curvatures for both these AdS braneworld black holes are
computed and studied as a function of the thermodynamic variables. Through this
analysis we illustrate an interesting dependence of the phase structures on the
braneworld parameter for these black holes.Comment: 21 pages, 10 figures and Appendix adde
An Exact Fluctuating 1/2-BPS Configuration
This work explores the role of thermodynamic fluctuations in the two
parameter giant and superstar configurations characterized by an ensemble of
arbitrary liquid droplets or irregular shaped fuzzballs. Our analysis
illustrates that the chemical and state-space geometric descriptions exhibit an
intriguing set of exact pair correction functions and the global correlation
lengths. The first principle of statistical mechanics shows that the possible
canonical fluctuations may precisely be ascertained without any approximation.
Interestingly, our intrinsic geometric study exemplifies that there exist exact
fluctuating 1/2-BPS statistical configurations which involve an ensemble of
microstates describing the liquid droplets or fuzzballs. The Gaussian
fluctuations over an equilibrium chemical and state-space configurations
accomplish a well-defined, non-degenerate, curved and regular intrinsic
Riemannian manifolds for all physically admissible domains of black hole
parameters. An explicit computation demonstrates that the underlying chemical
correlations involve ordinary summations, whilst the state-space correlations
may simply be depicted by standard polygamma functions. Our construction
ascribes definite stability character to the canonical energy fluctuations and
to the counting entropy associated with an arbitrary choice of excited boxes
from an ensemble of ample boxes constituting a variety of Young tableaux.Comment: Minor changes, added references, 30 pages, 4 figures, PACS numbers:
04.70.-s: Physics of black holes; 04.70.-Bw: Classical black holes; 04.50.Gh
Higher-dimensional black holes, black strings, and related objects; 04.60.Cf
Gravitational aspects of string theory, accepted for publication in JHE
Warm p-soup and near extremal black holes
We consider a model of D-dimensional supergravity coupled to elementary
p-branes. We use gravitational arguments to deduce the low energy effective
theory of N nearly parallel branes. This is a (p+1)-dimensional scalar field
theory, where the scalars represent the positions of the branes in their
transverse space. We propose that the same theory in a certain temperature
regime describes a `soup' of strongly interacting branes, giving a microscopic
description of near extremal black p-branes. We use natural approximations to
estimate the energy density of this soup as a function of the physical
parameters; N, temperature, brane tension and gravitational coupling. We also
characterise the horizon radius, measured in the metric natural to the branes,
with the thermal vev of the scalars. For both quantities we find agreement with
the corresponding supergravity black brane results. Surprisingly, beyond the
physical parameters, we are naturally able to reproduce certain irrational
factors such as pi's. We comment on how these ideas may explain why black hole
thermodynamics arises in gauge theories with holographic duals at finite
temperature.Comment: 32 pages, no figure
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