Gravitational mass and approximate Lie symmetries for the charged Hayward black hole

Abstract

Here we investigate the gravitational mass (energy) of the charged Hayward black hole utilizing the notion of the approximate version of the Lie symmetries. To investigate the approximate symmetries of the second-order perturbed geodesic equations and the gravitational mass for the charged Hayward black hole, we consider the black hole mass M and the charge Q as a small perturbation parameter ϵ. We recover the exact Lie symmetries as trivial second-order approximate Lie symmetries of the perturbed geodesic equations. The existence of the trivial second-order approximate symmetries of the perturbed geodesic equations provides the re-scaling of the arc-length parameter s, indicating that the gravitational energy in the charged Hayward black hole spacetime must be re-scaled by a factor that depends on the mass M, charge Q, coordinate r and the parameter l appears in the spacetime metric of charged Hayward black hole. We compare this energy re-scaling factor of the charged Hayward black hole to the energy re-scaling factor of the Reissner–Nordström black hole (Hussain et al., 2007). We notice that due to the presence of the Hayward parameter l, the gravitational energy in this black hole spacetime decreases.