31 research outputs found

### 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

### Thermodynamic Geometry and Topological Einstein-Yang-Mills Black Holes

From the perspective of the statistical fluctuation theory, we explore the
role of the thermodynamic geometries and vacuum (in)stability properties for
the topological Einstein-Yang-Mills black holes. In this paper, from the
perspective of the state-space surface and chemical Wienhold surface, we
provide the criteria for the local and global statistical stability of an
ensemble of topological Einstein-Yang-Mills black holes in arbitrary spacetime
dimensions $D\ge 5$. Finally, as per the formulations of the thermodynamic
geometry, we offer a parametric account of the statistical consequences in both
the local and global fluctuation regimes of the topological Einstein-Yang-Mills
black holes.Comment: 39 pages, 16 figures. Keywords: Thermodynamic Geometry; Topological
Einstein-Yang-Mills Black Holes; Higher Dimensional Gravity; Cosmological
Constant. Two typos correcte

### 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 state-space perspective to the black hole vacuum fluctuations. For a given black hole entropy, we explicate the intrinsic 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, namely, 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

### 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 $D_6$-$D_4$-$D_2$-$D_0$
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

### On the Thermodynamic Geometry of Hot QCD

We study the nature of the covariant thermodynamic geometry arising from the
free energy of hot QCD. We systematically analyze the underlying equilibrium
thermodynamic configurations of the free energy of 2- and 3-flavor hot QCD with
or without including thermal fluctuations in the neighborhood of the QCD
transition temperature. We show that there exists a well-defined thermodynamic
geometric notion for QCD thermodynamics. The geometry thus obtained has no
singularity as an intrinsic Riemannian manifold. We further show that there is
a close connection of this geometric approach with the existing studies of
correlations and quark number susceptibilities in hot QCD.Comment: 15 pages, 12 figures, Keywords: Thermodynamic Geometry, Hot QCD,
Quasi-particles, PACS: 12.38.-t; 05.70.Fh; 02.40.Ky; 12.40.E