The thermodynamic quantities of a black hole with an $f(R)$ global monopole

TL;DR

This paper investigates how $f(R)$ gravity modifies the thermodynamic properties of black holes with a global monopole, revealing similar qualitative behaviors to general relativity but with notable quantitative differences.

Contribution

It provides a comparative analysis of black hole thermodynamics in $f(R)$ gravity versus general relativity, highlighting the impact of gravitational theory generalization.

Findings

$f(R)$ gravity alters black hole thermodynamic quantities.

The shape of thermodynamic curves remains similar to general relativity.

Existence of small decaying black holes and large stable black holes at high temperatures.

Abstract

The thermodynamic quantities such as the local temperature, heat capacity, off-shell free energy and the stability of a black hole involving a global monopole within or outside the $f(R)$ gravity are examined. We compare the two classes of results to show the influence from the generalization of the general relativity. It is found that the $f(R)$ theory will modify the thermodynamic properties of black holes, but the shapes of curves for thermodynamic quantities with respect to the horizon are similar to the results within the frame of general relativity. In both cases there will exist a small black hole which will decay and a large stable black hole in the case that the temperatures are higher than their own critical temperature.