Charging Interacting Rotating Black Holes in Heterotic String Theory

TL;DR

This paper formulates a double Ernst system in heterotic string theory to describe interacting rotating black holes with various fields, and applies transformations to generate charged solutions with multiple fields.

Contribution

It introduces a novel double Ernst system formulation for heterotic string theory and applies a Harrison transformation to generate charged, rotating black hole solutions.

Findings

Derived explicit field configurations for interacting rotating black holes.

Showed how to generate multi-charged solutions using symmetry transformations.

Clarified the role of the Kalb-Ramond field and its possible torsion nature.

Abstract

We present a formulation of the stationary bosonic string sector of the whole toroidally compactified effective field theory of the heterotic string as a double Ernst system which, in the framework of General Relativity describes, in particular, a pair of interacting spinning black holes; however, in the framework of low--energy string theory the double Ernst system can be particularly interpreted as the rotating field configuration of two interacting sources of black hole type coupled to dilaton and Kalb--Ramond fields. We clarify the rotating character of the $B_{t\phi}$--component of the antisymmetric tensor field of Kalb--Ramond and discuss on its possible torsion nature. We also recall the fact that the double Ernst system possesses a discrete symmetry which is used to relate physically different string vacua. Therefore we apply the normalized Harrison transformation (a charging symmetry which acts on the target space of the low--energy heterotic string theory preserving the asymptotics of the transformed fields and endowing them with multiple electromagnetic charges) on a generic solution of the double Ernst system and compute the generated field configurations for the 4D effective field theory of the heterotic string. This transformation generates the $U(1)^n$ vector field content of the whole low--energy heterotic string spectrum and gives rise to a pair of interacting rotating black holes endowed with dilaton, Kalb--Ramond and multiple electromagnetic fields where the charge vectors are orthogonal to each other.