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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
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
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