Rotating black hole in 4D Einstein–Gauss–Bonnet massive gravity: Shadow and center of mass energy

Abstract

This work comprises the derivation of a rotating black hole metric by applying the modified Newman-Janis algorithm to a static four dimensional black hole in Einstein-Gauss–Bonnet massive gravity. We choose several parametric values to study the influence of graviton mass m and the Gauss–Bonnet parameter α on the horizon radii and photon sphere’s radii of the rotating and non-rotating black holes, respectively. By considering the Hamilton–Jacobi method, we construct the geodesic equations and by using Bardeen’s procedure of impact parameters, we study the effect of graviton mass on the effective potential, shadow, distortion and energy emission rate. We find that the graviton mass has a very significant effect on the shadow and related physical observables. In the vicinity of the black hole, we investigate the collision of two uncharged particles. We compute the energy of the particles in the center of mass frame for the static and rotating BH cases. Finally, the shadow diameter is compared with Sgr. A* to obtain the constraints on the black hole parameters.