Abstract
Abstract $f(R)$ theory is a modification of Einstein’s general relativity which has provided many interesting results in cosmology and astrophysics. To derive a black hole solution in this theory is difficult due to the fact that it contains fourth-order differential equations. In this study, we use the first reliable deviation from general relativity which is given by the quadratic form of $f(R)=R+\beta R^2$, where $\beta$ is a dimensional parameter. We calculate the energy conditions of charged black holes and show that they are all satisfied for the Taub–NUT spacetime. Finally, we study some thermodynamic quantities such as entropy, temperature, specific heat, and Gibbs free energy. The calculations of heat capacity and free energy show that the charged Taub–NUT black hole has positive values, which means that it has thermal stability.
Highlights
The Hilbert-Einstein Lagrangian which involves higher order corrections of Ricci scalar has been used a long time ago as a result of the quantum correction to the gravitational field of the matter source [1]
Scientists discovered that the terms which are related to the quantum higher order corrections are responsible for the accelerating expansion rate of our universe at large structures. This phenomenon has been investigated at the fourth order of f (R) [7,8,9,10,11,12,13,14,15]
We are going to consider f (R) = R + βR2 which we consider as a physical model due to the following: For this theory, in the early universe, the R2 term is dominant and it can lead to the so-called Starobinsky inflation [2]
Summary
The Hilbert-Einstein Lagrangian which involves higher order corrections of Ricci scalar has been used a long time ago as a result of the quantum correction to the gravitational field of the matter source [1] Due to this feature, it was thought that such terms are successful to describe the early epoch of the growth of our universe. The main purpose of this work is to use the non-charged and charged gravitational field equations for f (R) gravity theory with its quadratic form in Taub-NUT spacetime and try to find new solutions.
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