Rotating Intersecting M-Branes

TL;DR

This paper develops a systematic framework for constructing non-extreme rotating intersecting M-brane solutions in eleven-dimensional supergravity, which upon toroidal compactification yield rotating black holes. It identifies how rotation modifies the harmonic functions and non-extremality functions, and presents a two-step algorithm to assemble the full eleven-dimensional metric by incorporating multiple M-branes and possible boosts along common intersections. The authors explicitly uplift two- and three-brane configurations from lower-dimensional rotating black holes, outline the structure for four-brane intersections, and analyze the BPS limits, distinguishing singular from regular cases. The results illuminate how angular momenta and M-theory charge sources contribute to the geometry and potential entropy of rotating non-extreme BPS black holes, offering a bridge between brane physics and black hole thermodynamics.

Abstract

We present intersecting p-brane solutions of eleven-dimensional supergravity (M-branes) which upon toroidal compactification reduce to non-extreme ``rotating'' black holes. We identify harmonic functions, associated with each M-brane, and non-extremality functions, specifying a deviation from the BPS limit. These functions are modified due to the angular momentum parameters, which specify the rotation along the transverse directions of the M-branes. We spell out the intersection rules for the eleven-dimensional space-time metric for intersecting (up to three) rotating M-brane configurations (and a boost along the common intersecting direction).