The Black Branes of M-theory
M. J. Duff, H. Lu, C. N. Pope
TL;DR
The paper presents a universal non-extremal construction for black $p$-branes in M-theory by truncating eleven-dimensional supergravity to a set of scalars and form fields, and derives closed-form non-extremal solutions. It provides explicit expressions for the Hawking temperature $T$ and entropy $S$ for single-scalar, dyonic, and multi-scalar branes, showing how charges renormalize the extremal solutions through hyperbolic functions of boost parameters. The results extend known extremal (supersymmetric) brane solutions to generic non-extremal cases and establish how $T$ and $S$ depend on the dilaton charges, with extremality corresponding to a saturated Bogomol'nyi bound. The work sets the stage for microscopic entropy derivations via $D$-brane techniques and tests of M-theory against black-brane thermodynamics.
Abstract
We present a class of black $p$-brane solutions of M-theory which were hitherto known only in the extremal supersymmetric limit, and calculate their macroscopic entropy and temperature.