Black and White holes in four-dimensional Chern-Simons gravity

TL;DR

This paper explores black hole solutions in a novel four-dimensional Chern-Simons gravity theory derived from a higher-dimensional model, revealing black and white hole solutions with unique properties related to the cosmological constant and a parameter C.

Contribution

It introduces a new four-dimensional gravitational action from a higher-dimensional Chern-Simons framework and analyzes its black hole solutions, including black and white holes, with novel dependence on a parameter C.

Findings

Existence of Schwarzschild-de Sitter black holes for negative C

White hole solutions obtained via a PT transformation and mass reversal

Cosmological constant inversely related to the square of the compactification radius

Abstract

We discuss a four-dimensional gravitational action which was obtained replacing a Randall-Sundrum type metric in the so called five-dimensional Einstein-Chern-Simons gravity action. We studied black hole solutions of the corresponding 4-dimensional gravitational field equations. It is found that for a spherically symmetric metric such equations lead to a spacetime with a cosmological constant inversely proportional to the square of the compactification radius and to one solution dependent on an arbitrary constant C. If this constant is negative, we find a Schwarzschid-de Sitter black hole. If C is positive, the solution can be understood as a white hole solution which is obtained applying to the solution with C<0 the discrete coordinate transformation PT accompanied by the transformation C -C, with C>0, corresponding to a transformation known as mass reversal.