Abstract
We consider Maxwell-f(R) gravity and obtain an exact charged black hole solution with dynamic curvature in D-dimensions. Considering a spherically symmetric metric ansatz and without specifying the form of f(R) we find a general black hole solution in D-dimensions. This general black hole solution can reduce to the Reissner–Nordström (RN) black hole in D-dimensions in Einstein gravity and to the known charged black hole solutions with constant curvature in f(R) gravity. Restricting the parameters of the general solution we get polynomial solutions which reveal novel properties when compared to RN black holes. Specifically we study the solution in (3+1)-dimensions in which the form of f(R) can be solved explicitly giving a dynamic curvature and compare it with the RN black hole. We also carry out a detailed study of its thermodynamics.
Highlights
At very early times, to avoid restricting the gravitational Lagrangian to be only a linear function of R, variable modified theories of gravity that contain some of the four possible second-order curvature invariants were proposed with the effects of quadratic Lagrangians
Considering the gravitational collapse, one would expect all the matter present to be absorbed by the black hole, so the final state should be vacuum except for the presence of electromagnetic fields associated with the black hole
Before we study the thermodynamics of our solution in f (R) gravity, we first review the First Law for RN black hole in Einstein gravity to compare
Summary
To avoid restricting the gravitational Lagrangian to be only a linear function of R, variable modified theories of gravity that contain some of the four possible second-order curvature invariants were proposed with the effects of quadratic Lagrangians. In this work, considering a spherically symmetric metric ansatz with gtt grr = −1, without specifying the form of the function f (R), we obtain exact charged black hole solutions in general D-dimensional f (R) gravity. Page 3 of 16 346 motivation to consider the specific form gtt grr = −1 of the metric, is to be able to compare the resulting exact solutions with the RN black holes in GR and study what is the effect of the f (R) function on the known solutions in GR. We will show that even in higher dimensional cases, the effective cosmological constant can be defined as the coefficient of r 2 term in the metric function redefining the length scale of the theory.
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