General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String

TL;DR

This paper derives the most general rotating black hole solutions in five-dimensional heterotic string theory compactified on a torus, characterized by 27 charges and rotational parameters, expanding understanding of black hole configurations in string theory.

Contribution

It provides a comprehensive construction of the most general rotating black hole solutions in five-dimensional heterotic string vacua using symmetry transformations, including explicit charge and rotation parameters.

Findings

Derived the explicit form of the general rotating black hole solution.

Identified the parameter space with 27 charges and two rotational parameters.

Analyzed deviations from BPS saturation in these solutions.

Abstract

We present the most general rotating black hole solution of five-dimensional N=4 superstring vacua that conforms to the ``no hair theorem''. It is chosen to be parameterized in terms of massless fields of the toroidally compactified heterotic string. The solutions are obtained by performing a subset of O(8,24) transformations, i.e., symmetry transformations of the effective three-dimensional action for stationary solutions, on the five-dimensional (neutral) rotating solution parameterized by the mass m and two rotational parameters $l_1$ and $l_2$. The explicit form of the generating solution is determined by three $SO(1,1)\subset O(8,24)$ boosts, which specify two electric charges $Q_1^{(1)}, Q_{2}^{(2)}$ of the Kaluza-Klein and two-form U(1) gauge fields associated with the same compactified direction, and the charge Q (electric charge of the vector field, whose field strength is dual to the field strength of the five-dimensional two-form field). The general solution, parameterized by 27 charges, two rotational parameters and the ADM mass compatible with the Bogomol'nyi bound, is obtained by imposing $[SO(5)\times SO(21)]/[SO(4)\times SO(20)]\subset O(5,21)$ transformations, which do not affect the five-dimensional space-time. We also analyze the deviations from the BPS-saturated limit.