Anisotropic Black Holes in Einstein and Brane Gravity

TL;DR

This paper presents exact anisotropic black hole solutions in Einstein and brane gravity, demonstrating how off-diagonal metrics and anholonomic frames can produce novel horizon geometries and effective charges consistent with known theorems.

Contribution

It introduces a method to generate anisotropic black hole solutions using off-diagonal metrics and applies this to brane-world scenarios with effective electromagnetic-like charges.

Findings

Exact anisotropic black hole solutions with ellipsoidal horizons.

Off-diagonal metrics can be transformed into diagonal forms with anisotropic parameters.

Anisotropic deformations of Reissner-Nordstrom solutions are valid on the brane.

Abstract

We consider exact solutions of Einstein equations defining static black holes parametrized by off-diagonal metrics which by anholonomic mappings can be equivalently transformed into some diagonal metrics with coefficients being very similar to those from the Schwarzschild and/or Reissner-N\"ordstrom solutions with anisotropic renormalizations of constants. We emphasize that such classes of solutions, for instance, with ellipsoidal symmetry of horizons, can be constructed even in general relativity theory if off-diagonal metrics and anholonomic frames are introduced into considerations. Such solutions do not violate the Israel's uniqueness theorems on static black hole configurations because at long radial distances one holds the usual Schwarzschild limit. We show that anisotropic deformations of the Reissner-N\"ordstrom metric can be an exact solution on the brane, re-interpreted as a black hole with an effective electromagnetic like charge anisotropically induced and polarized by higher dimension gravitational interactions.