Extending the geometric deformation: New black hole solutions

TL;DR

This paper extends the Minimal Geometric Deformation approach to derive new black hole solutions with higher-order tidal charge terms, revealing how extra-dimensional effects influence black hole horizons.

Contribution

It introduces a generalized exterior black hole solution incorporating higher-order tidal charge effects using an extended geometric deformation method.

Findings

The horizon is located inside the Schwarzschild radius, indicating weaker gravity due to extra dimensions.

The solution includes higher-order terms in the tidal charge, generalizing previous models.

Extra-dimensional effects modify the black hole's exterior geometry.

Abstract

We use the extension of the Minimal Geometric Deformation approach, recently developed to investigate the exterior of a self-gravitating system in the Braneworld, to identified a master solution for the deformation undergone by the radial metric component when time deformations are produced by bulk gravitons. A specific form for the temporal deformation is used to generate a new exterior solution with a tidal charge $Q$. The main feature of this solution is the presence of higher-order terms in the tidal charge, thus generalizing the well known tidally charged solution. The horizon of the black hole lies inside the Schwarzschild radius, $h<r_s=2\,{\cal M}$, indicating that extra-dimensional effects weaken the gravitational field.