Non-extreme black holes from non-extreme intersecting M-branes

TL;DR

This paper constructs non-extreme generalisations of intersecting M-brane (p-brane) solutions in eleven dimensions, showing how a single non-extremality parameter μ and charge boosts generate static non-extreme black holes in D=4–9 via toroidal compactification. By deforming known BPS-saturated intersecting brane configurations, the authors derive explicit 11D metrics, four-form fields, and reduced D-dimensional black-hole geometries with multiple charges, and they provide horizon-area expressions and universal mass-entropy relations. The work unifies the description of non-extreme black holes across dimensions through a common harmonic-function framework and a clear dimensional-reduction scheme, enabling analysis of both extremal and near-extremal regimes. These results lay groundwork for interpreting black-hole entropy in M-theory terms and for exploring thermodynamic relations in a brane-bound-state context.

Abstract

We present non-extreme generalisations of intersecting p-brane solutions of eleven-dimensional supergravity which upon toroidal compactification reduce to non-extreme static black holes in dimensions D=4, D=5 and 5<D<10, parameterized by four, three and two charges, respectively. The D=4 black holes are obtained either from non-extreme configuration of three intersecting five-branes with a boost along the common string or from non-extreme intersecting system of two two-branes and two five-branes. The D=5 black holes arise from three intersecting two-branes or from a system of intersecting two-brane and five-brane with a boost along the common string. Five-brane and two-brane with a boost along one direction reduce to black holes in D=6 and D=9, respectively, while D=7 black hole can be interpreted in terms of non-extreme configuration of two intersecting two-branes. We discuss the expressions for the corresponding masses and entropies.