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

## TL;DR

This paper investigates the stability and fragmentation of black holes with $f(R)$ global monopoles under the generalized uncertainty principle, revealing conditions under which fragmentation occurs or is suppressed.

## Contribution

It introduces a generalized entropy analysis for $f(R)$ monopole black holes under GUP, showing stability without GUP and potential fragmentation with GUP-induced deviations.

## Key findings

- Black holes remain stable without GUP due to entropy considerations.
- GUP can induce black hole fragmentation under certain conditions.
- Significant deviations from general relativity lead to asymmetric black hole fragmentation.

## Abstract

The fragmentation of black hole containing $f(R)$ global monopole under GUP is studied. We focus on that the black hole breaks into two parts. 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 breaking because the entropy difference is negative without the generalization. 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 the case that the mass of one fragmented black hole is extremely small and the other one is extremely large.