The sound damping constant for generalized theories of gravity

TL;DR

This paper explores how the sound damping constant in conformal theories derived from gravity is affected by generalized theories of gravity, extending known results from Einstein gravity and linking it to gravitational couplings.

Contribution

It demonstrates the modification of the sound damping constant in generalized gravity theories and expresses it as a ratio of gravitational couplings, expanding understanding beyond Einstein gravity.

Findings

The near-horizon and boundary metrics exhibit equivalent hydrodynamic behavior.

The sound damping constant is modified in generalized theories and can be expressed via gravitational couplings.

The ratio of couplings for sound differs from shear-related ratios.

Abstract

The near-horizon metric for a black brane in Anti-de Sitter (AdS) space and the metric near the AdS boundary both exhibit hydrodynamic behavior. We demonstrate the equivalence of this pair of hydrodynamic systems for the sound mode of a conformal theory. This is first established for Einstein's gravity, but we then show how the sound damping constant will be modified, from its Einstein form, for a generalized theory. The modified damping constant is expressible as the ratio of a pair of gravitational couplings that are indicative of the sound-channel class of gravitons. This ratio of couplings differs from both that of the shear diffusion coefficient and the shear viscosity to entropy ratio. Our analysis is mostly limited to conformal theories but suggestions are made as to how this restriction might eventually be lifted.