Eling-Oz Formula for Exotic Hairy Black Holes

TL;DR

This paper verifies the Eling-Oz formula for bulk viscosity in exotic black hole holography across various temperatures, confirming its accuracy and critical behavior near phase transitions.

Contribution

It extends the validation of the Eling-Oz formula to exotic black holes over a broad temperature range, including near critical points.

Findings

Eling-Oz formula accurately predicts bulk viscosity for exotic black holes.

The formula reproduces critical behavior near phase transition points.

Validation spans high to low temperatures, confirming its broad applicability.

Abstract

We checked Eling-Oz formula [1] for the bulk viscosity of the holographic fluid dual to the exotic black holes [2]. Initially, Eling and Oz argued that the formula is valid in the high temperature and adiabatic limits. In [3] the validity of the formula for $\caln=2^*$ plasma and cascading gauge theory was pushed forward for arbitrary temperatures. We successfully verified the formula with the computations of the bulk viscosity [4,5] for a wide range of the temperatures. Moreover, it correctly reproduces the critical behavior in the vicinity of the critical point, where the bulk-to-shear viscosity diverges.