On exact analytical solution of Einstein–Maxwell-scalar field equations

Abstract

The exact analytical solution of Einstein–Maxwell-scalar (EMS) field equations has been explored which covers several well-known solutions such as the Reissner–Nordström, Schwarzschild-MOG (Modified Gravity), Janis–Newman–Winicour, and Schwarzschild solutions. It has been assumed that the interactions between the tensor, vector, and scalar fields are negligible. The newly obtained solution is characterized by three free parameters as the total mass M , electric (magnetic) charge Q e ( Q m ), and scalar charge C (or n parameter) of the gravitational compact object. It is also shown that dual solution for the vector potential A ϕ = Q m cos θ is satisfied by the EMS field equations and the electric charge can be safely replaced by magnetic charge Q m . Finally, we have studied curvature invariants and test particle motion around the gravitational source described the obtained new spacetime metric. We have also provided analysis of degeneracy values of spin parameter of the rotating Kerr black hole and charge parameter of compact object described by the new spacetime metric through comparison of radii of ISCO, photonsphere and energy efficiency. It is shown that new black hole solution in Einstein–Maxwell-scalar field theory can mimic spin parameter of the Kerr black hole up to a ∗ ≲ 0 . 6 while the astrophysical black hole’ observations that it reaches up to a ∗ ≲ 0 . 99 . Consequently, one may conclude that the obtained new black hole solution can be considered as realistic candidate for the astrophysical black holes with a ∗ ≲ 0 . 6 .