Abstract
We report exact black hole solutions in asymptotically flat or (A)dS four-dimensional spacetime with a conformally coupled self-interacting scalar field in f(R) gravity. We first consider the asymptotically flat model f(R) = R -2alpha sqrt{R} and derive an exact black hole solution. Then, we consider the asymptotically (A)dS model f(R) =R -2 Lambda -2 alpha sqrt{R-4 Lambda } and derive an exact black hole solution. In both cases the modified gravity parameter alpha , which has the dimension of the inverse mass, cannot be set to zero and the self-interacting potential is determined from the Klein–Gordon equation, preserving the conformal invariance. The thermodynamics of the solutions is also studied.
Highlights
Differences between general relativity (GR) and alternative theories are expected to occur for strong gravitational fields, such as the ones created by different compact objects like neutron stars, strange stars and black holes
The scalar field is introduced in the action as a matter field in the way it was done in the GR context [1,2,3,5] and we study its effect on a metric ansatz solving the field equations
Solving the full system of field equations we find that this parameter contributes to the mass of the black hole, specifies the strength of the scalar field and influences the thermodynamical properties of the solutions
Summary
We discuss the GR black hole solutions with a scalar field conformally coupled to gravity. The first solution was found by Bocharova, Bronnikov and Melnikov and independently by Bekenstein, called the BBMB black hole [1,2,3]
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