Tension Perturbations of Black Brane Spacetimes

TL;DR

This paper introduces the concept of tension in black brane spacetimes, explores its perturbations, and derives a first law relating tension changes to horizon properties and charges, with implications for black brane evaporation.

Contribution

It defines a new tension parameter for black branes and derives a law relating tension perturbations to horizon and charge variations, extending black hole thermodynamics.

Findings

Tension decreases as black branes evaporate.

A law relating tension perturbations to surface gravity and horizon area is derived.

The results apply to arbitrary stress-energy sources governed by a Hamiltonian.

Abstract

We consider black-brane spacetimes that have at least one spatial translation Killing field that is tangent to the brane. A new parameter, the tension of a spacetime, is defined. The tension parameter is associated with spatial translations in much the same way that the ADM mass is associated with the time translation Killing field. In this work, we explore the implications of the spatial translation symmetry for small perturbations around a background black brane. For static charged black branes we derive a law which relates the tension perturbation to the surface gravity times the change in the the horizon area, plus terms that involve variations in the charges and currents. We find that as a black brane evaporates the tension decreases. We also give a simple derivation of a first law for black brane spacetimes. These constructions hold when the background stress-energy is governed by a Hamiltonian, and the results include arbitrary perturbative stress-energy sources.