On the Bekenstein-Hawking area law for black objects with conical singularities

TL;DR

This paper demonstrates that the Bekenstein-Hawking area law remains valid for asymptotically flat black objects with conical singularities when using the correct thermodynamical variables, and clarifies the distinction between mass definitions.

Contribution

It shows that the Bekenstein-Hawking law holds for black objects with conical singularities when proper thermodynamic variables are used, and clarifies the relationship between different mass measures.

Findings

The Bekenstein-Hawking law applies with conical singularities when using appropriate variables.

The thermodynamic mass differs from the ADM mass by the energy of the conical singularity.

Examples include the double-Schwarzschild solution, Einstein-Maxwell diholes, and the black ring.

Abstract

We argue that, when working with the appropriate set of thermodynamical variables, the Bekenstein-Hawking law still holds for asymptotically flat black objects with conical singularities. The mass-energy which enters the first law of thermodynamics does not, however, coincide with the ADM mass; it differs from the latter by the energy associated with the conical singularity, as seen by an asymptotic, static observer. These statements are supported by a number of examples: the Bach-Weyl (double-Schwarzschild) solution, its dihole generalisation in Einstein-Maxwell theory and the five dimensional static black ring.