Radiating Kerr-Newman black hole in $f(R)$ gravity

TL;DR

This paper derives an exact radiating Kerr-Newman black hole solution in $f(R)$ gravity, revealing additional cosmological horizons and modifications to the ergosphere shape due to constant curvature effects.

Contribution

It presents a novel exact solution for radiating Kerr-Newman black holes in $f(R)$ gravity, including the effects of constant curvature and additional horizons.

Findings

Existence of an extra cosmological horizon in $f(R)$ gravity.

The shape of the ergosphere is affected by the constant curvature $R_0$.

Recovery of known Kerr-Newman solutions in the appropriate limits.

Abstract

We derive an exact radiating Kerr-Newman like black hole solution, with constant curvature $R=R_0$ imposed, to {\it metric} $f(R)$ gravity via complex transformations suggested by Newman-Janis. This generates a geometry which is precisely that of radiating Kerr-Newman-de Sitter / anti-de Sitter with the $f(R)$ gravity contributing an $R_0$ cosmological-like term. The structure of three horizon-like surfaces, {\it viz.} timelike limit surface, apparent horizon and event horizon, are determined. We demonstrate the existence of an additional cosmological horizon, in $f(R)$ gravity model, apart from the regular black hole horizons that exist in the analogous general relativity case. In particular, the known stationary Kerr-Newman black hole solutions of $f(R)$ gravity and general relativity are retrieved. We find that the timelike limit surface becomes less prolate with $R_0$ thereby affecting the shape of the corresponding ergosphere.