Slowly Rotating Black Holes in 4D Einstein Gauss-Bonnet Gravity

TL;DR

This paper derives slowly rotating black hole solutions in 4D Einstein Gauss-Bonnet gravity and analyzes how their physical properties differ from those predicted by general relativity across different cosmological backgrounds.

Contribution

It provides the first explicit construction of slowly rotating black holes in 4D Einstein Gauss-Bonnet gravity for various cosmological constants and compares their properties to Einstein gravity.

Findings

Minimum black hole mass in negative or zero cosmological constant cases.

Maximum and minimum mass bounds in positive cosmological constant case.

Deviations from general relativity are most significant in low-mass regimes.

Abstract

Since the recent derivation of a well-defined $D\rightarrow 4$ limit for regularized 4D Einstein Gauss-Bonnet (4DEGB) gravity, there has been considerable interest in testing it as an alternative to Einstein's general theory of relativity. In this paper we construct slowly rotating black hole solutions for 4DEGB gravity in asymptotically flat, de Sitter, and anti-de Sitter spacetimes. At leading order in the rotation parameter, exact solutions of the metric functions are derived and studied for all three of these cases. We compare how physical properties (innermost stable circular orbits, photon rings, black hole shadow, etc.) of the solutions are modified by varying coupling strengths of the 4DEGB theory relative to standard Einstein gravity results. We find that a vanishing or negative cosmological constant in 4DEGB gravity enforces a minimum mass on the black hole solutions, whereas a positive cosmological constant enforces both a minimum \textit{and} maximum mass with a horizon root structure directly analogous to the Reissner-Nordstr\"om de Sitter spacetime. Besides this, many of the physical properties are qualitatively similar to general relativity, with the greatest deviations typically being found in the low (near-minimal) mass regime.