ADM masses for black strings and p-branes

TL;DR

This paper derives a general ADM mass formula for spherically symmetric black solutions and applies it to black strings and p-branes, clarifying mass calculation methods and the validity of the Bogomol'nyi bound.

Contribution

The paper introduces a new ADM mass formula applicable to a broad class of black objects and demonstrates its use on black strings and p-branes across various dimensions.

Findings

Explicit ADM mass calculations for black strings and p-branes.

Verification of the Bogomol'nyi equation for these solutions.

Observation that ADM mass can be directly obtained from metric asymptotics only for p=0.

Abstract

An ADM mass formula is derived for a wide class of black solutions with certain spherical symmetry. By applying this formula, we calculate the ADM masses for recently discovered black strings and $p$-branes in diverse dimensions. By this, the Bogolmol'nyi equation can be shown to hold explicitly. A useful observation is made for non-extremal black $p$-branes that only for $p = 0$, i.e. for a black hole, can its ADM mass be read directly from the asymptotic behaviour of the metric component $g_{00}$.