Unruh effect in curved space-time and hydrodynamics

TL;DR

This paper explores the Unruh effect in curved space-time by analyzing an accelerated fluid in (A)dS space, establishing a duality between hydrodynamics and gravity, and relating transport coefficients across different geometries.

Contribution

It introduces a hydrodynamic framework for accelerated fluids in (A)dS space and links it to higher-dimensional gravity, revealing new dualities and temperature relations.

Findings

(A)dS vacuum corresponds to a thermal bath with acceleration-dependent temperature.

Established a direct relationship between transport coefficients in flat and curved space-times.

Developed a duality connecting hydrodynamics and gravity in curved backgrounds.

Abstract

We consider an accelerated relativistic fluid in four-dimensional (anti-)de Sitter space-time. Analyzing only hydrodynamic equations, we construct the equilibrium stress-energy tensor. We confirm that (A)dS vacuum corresponds to a thermal bath in the accelerated frame with a temperature, depending on the acceleration in a flat higher-dimensional (namely, five-dimensional) space, in which curved space-times are embedded. We develop the duality between hydrodynamics and gravity finding a direct relationship between the transport coefficients in flat and curved space-times.