Near-BPS-Saturated Rotating Electrically Charged Black Holes as String States

TL;DR

This paper constructs explicit solutions for rotating, electrically charged black holes in higher-dimensional heterotic string theory, and relates their near-extreme thermodynamic entropy to microscopic string states with angular momenta.

Contribution

It provides a unified method to generate rotating charged black hole solutions in D-dimensional heterotic string theory and connects near-BPS entropy to string microstates.

Findings

Solutions valid for D=4 to 9 dimensions.

Near-extreme entropy matches microscopic string state counting.

Angular momenta correspond to world-sheet currents.

Abstract

We construct generating solutions for general D-dimensional ($4 \le D \le 9$) rotating, electrically charged, black holes in the effective action of toroidally compactified heterotic (or Type IIA) string. The generating solution is parameterized by the ADM mass, two electric charges and $[{D-1}\over 2]$ angular momenta (as well as the asymptotic values of one toroidal modulus and the dilaton field). For $D \ge 6$, those are generating solutions for {\it general} black holes in toroidally compactified heterotic (or type IIA) string. Since in the BPS-limit (extreme limit) these solutions have singular horizons or naked singularities, we address the near extreme solutions with all the angular momenta small enough. In this limit, the thermodynamic entropy can be cast in a suggestive form, which has a qualitative interpretation as microscopic entropy of (near)-BPS-saturated charged string states of toroidally compactified heterotic string, whose target-space angular momenta are identified as $[{{D-1}\over 2}]$ U(1) left-moving world-sheet currents.