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

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.