Ehlers-Harrison transformations and black holes in Dilaton-Axion Gravity with multiple vector fields

TL;DR

This paper develops a new class of static black hole solutions in dilaton-axion gravity with multiple vector fields, revealing how their horizons and singularities depend on charge configurations and symmetries.

Contribution

It derives a general static black hole solution with multiple parameters using SO(2,2+p) symmetry, extending previous models in dilaton-axion gravity.

Findings

Black hole solutions depend on charge alignment and parameters.

Inner horizon behavior varies with charge configuration.

Extremal solutions with orthogonal charges have variable horizon radii.

Abstract

Dilaton-axion gravity with $p U(1)$ vector fields is studied on space-times admitting a timelike Killing vector field. Three-dimensional sigma-model is derived in terms of K\"ahler geometry, and holomorphic representation of the SO(2,2+p) global symmetry is constructed. A general static black hole solution depending on $2p+5$ parameters is obtained via SO(2,2+p) covariantization of the Schwarzschild solution. The metric in the curvature coordinates looks as the variable mass Reissner-Nordstr\"om one and generically possesses two horizons. The inner horizon is pushed to the singularity if electric and magnetic SO(p) charge vectors are parallel. For non-parallel charges the inner horizon has a finite area except for an extremal limit when this property is preserved only for orthogonal charges. Extremal dyon configurations with orthogonal charges have finite horizon radii continuously varying from zero to the ADM mass. New general solution is endowed with a NUT parameter, asymptotic values of dilaton and axion, and a gauge parameter which can be used to ascribe any given value to one of scalar charges.