The fragmentation instability of a black hole with f(R) global monopole under GUP

Abstract

Having studied the fragmentation of the black holes containing f(R) global monopole under the generalized uncertainty principle (GUP), we show the influences from this kind of monopole, f(R) theory, and GUP on the evolution of black holes. We focus on the possibility that the black hole breaks into two parts by means of the second law of thermodynamics. We derive the entropies of the initial black hole and the broken parts while the generalization of Heisenberg’s uncertainty principle is introduced. We find that the f(R) global monopole black hole keeps stable instead of splitting without the generalization because the entropy difference is negative. The fragmentation of the black hole will happen if the black hole entropies are limited by the GUP and the considerable deviation from the general relativity leads to the case that the mass of one fragmented black hole is smaller and the other one’s mass is larger.