General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String

TL;DR

This work provides a complete construction of the most general rotating five-dimensional black hole in toroidally compactified heterotic string vacua by exploiting duality symmetries. Beginning with a neutral 5D Kerr solution, the authors apply three $SO(1,1)$ boosts in the three-dimensional reduced theory to generate three charges and then extend with $[SO(5)\times SO(21)]/[SO(4)\times SO(20)]$ coset transformations to reach 27 charges while keeping the 5D spacetime fixed. They present an explicit generating solution with the full set of 5D fields, gauge and two-form sectors, and horizon structure, and they analyze the BPS saturated limit and infinitesimal deviations from it, including exact expressions for the horizon area and mass in terms of charges. The results unify known BPS configurations and illuminate how moduli and dualities shape the macroscopic properties of general charged rotating black holes in this string theory context.

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.