Accelerating Branes and Brane Temperature

TL;DR

This paper introduces a dimensionless parameter to interpret brane acceleration as local Unruh temperature, analyzing various brane configurations and their thermal properties in different spacetimes.

Contribution

It defines a new parameter lambda to relate brane acceleration to temperature and applies it to diverse brane scenarios in various spacetimes.

Findings

Lambda is small for valid Unruh temperature interpretation

Brane temperature matches Gibbons-Hawking temperature in specific cases

Different brane configurations exhibit distinct thermal behaviors

Abstract

We define the local acceleration and jerk of a relativistic brane in an ambient spacetime, and construct from them a dimensionless parameter lambda that must be small for an interpretation of brane acceleration as local Unruh temperature. As examples, we discuss (i) open rotating branes, for which lambda>1 (ii) closed spherical branes expanding in Minkowski spacetime, for which lambda=0 when the worldvolume is either an Einstein static universe or de Sitter space, in which case the brane temperature equals the Gibbons-Hawking temperature, (iii) closed spherical branes in anti-de Sitter spacetime, for which a maximally symmetric worldvolume is anti-de Sitter, Minkowski or de Sitter according to whether the magnitude of the brane acceleration is less than, equal to or greater than a `critical' value, and (iv) the BTZ black hole, viewed as a membrane.