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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.