Hydrodynamics of a 5D Einstein-dilaton black hole solution and the corresponding BPS state

TL;DR

This paper constructs and analyzes a 5D Einstein-dilaton black hole solution using potential reconstruction, explores its hydrodynamic properties via fluid/gravity duality, and confirms its BPS stability and supersymmetric features.

Contribution

It introduces a novel analytic 5D black hole solution with scalar fields and studies its hydrodynamics and stability, including BPS properties and supersymmetry.

Findings

Derived a new analytic 5D black hole solution with scalar fields.

Analyzed hydrodynamic properties, including shear viscosity to entropy density ratio.

Confirmed the solution's stability and BPS nature through energy and spinor analyses.

Abstract

We apply the potential reconstruction approach to generate a series of asymptotically AdS (aAdS) black hole solutions, with a self-interacting bulk scalar field. Based on the method, we reproduce the pure AdS solution as a consistency check and we also generate a simple analytic 5D black hole solution. We then study various aspects of this solution, such as temperature, entropy density and conserved charges. Furthermore, we study the hydrodynamics of this black hole solution in the framework of fluid/gravity duality, e.g. the ratio of the shear viscosity to the entropy density. In a degenerate case of the 5D black hole solution, we find that the c function decreases monotonically from UV to IR as expected. Finally, we investigate the stability of the degenerate solution by studying the bosonic functional energy of the gravity and the Witten-Nester energy $E_{WN}$. We confirm that the degenerate solution is a BPS domain wall solution. The corresponding superpotential and the solution of the killing spinor equation are found explicitly.