Rotating black holes in Einstein-Dilaton-Gauss-Bonnet gravity with finite coupling

TL;DR

This paper derives an approximate rotating black hole solution in Einstein-Dilaton-Gauss-Bonnet gravity, incorporating finite coupling effects, and analyzes its geometrical and geodesic properties relevant for testing gravity theories with astrophysical observations.

Contribution

It provides a closed-form, higher-order correction to rotating black holes in Einstein-Dilaton-Gauss-Bonnet gravity, extending previous leading-order results and enabling near-maximum coupling analysis.

Findings

Derived a stationary, axisymmetric black hole solution quadratic in spin and seventh order in coupling.

Computed geometrical properties like dilaton charge, moment of inertia, and quadrupole moment.

Analyzed geodesic structure, including ISCO and epicyclic frequencies, for observational tests.

Abstract

Among various strong-curvature extensions to General Relativity, Einstein-Dilaton-Gauss-Bonnet gravity stands out as the only nontrivial theory containing quadratic curvature corrections while being free from the Ostrogradsky instability to any order in the coupling parameter. We derive an approximate stationary and axisymmetric black-hole solution of this gravitational theory in closed form, which is quadratic in the black-hole spin angular momentum and of seventh order in the coupling parameter of the theory. This extends previous work that obtained the corrections to the metric only at the leading order in the coupling parameter, and allows us to consider values of the coupling parameter close to the maximum permitted by theoretical constraints. We compute some geometrical properties of this solution, such as the dilaton charge, the moment of inertia and the quadrupole moment, and its geodesic structure, including the innermost-stable circular orbit and the epicyclic frequencies for massive particles. The latter represent a valuable tool to test General Relativity against strong-curvature corrections through observations of the electromagnetic spectrum of accreting black holes.