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