Multi-horizons black hole solutions, photon sphere and perihelion shift in weak ghost-free Gauss-Bonnet theory of gravity

TL;DR

This paper derives new black hole solutions in ghost-free Gauss-Bonnet gravity, analyzes their properties including horizons and thermodynamics, and investigates photon spheres and perihelion shifts to provide observable predictions for the theory.

Contribution

It introduces new spherically symmetric black hole solutions in GFGB gravity and explores their physical and observable properties, extending previous research.

Findings

Black hole solutions with multiple horizons were found.

Thermodynamical quantities are consistent with prior studies.

Photon spheres and perihelion shifts were characterized in the weak GFGB regime.

Abstract

Among the modified gravitational theories, the ghost-free Gauss-Bonnet (GFGB) theory of gravity has been considered from the viewpoint of cosmology. The best way to check its applicability could be to elicit observable predicts which give guidelines or limitations on the theory, which could be contrasted with the actual observations. In the present study, we derive consistent field equations for GFGB and by applying the equations to a spherically symmetric space-time, we obtain new spherically symmetric black hole (BH) solutions. We study the physical properties of these BH solutions and show that the obtained space-time possesses multi-horizons and the Gauss-Bonnet invariants in the space-time are not trivial. We also investigate the thermodynamical quantities related to these BH solutions and we show that these quantities are consistent with what is known in the previous works. Finally, we study the geodesic equations of these solutions which give the photon spheres and we find the perihelion shift for weak GFGB. In addition, we calculate the first-order GFGB perturbations in the Schwarzschild solution and new BH solutions and show that we improve and extend existing results in the past literature on the spherically symmetric solutions.