# Overspinning Kerr-MOG black holes by test fields and the third law of black hole dynamics

## TL;DR

This paper investigates the stability of Kerr-MOG black holes against test fields, showing that while they can be overspun without backreaction, the cosmic censorship and third law hold when backreaction effects are considered for certain parameter ranges.

## Contribution

It demonstrates the impact of backreaction effects on the validity of cosmic censorship and the third law for Kerr-MOG black holes, extending previous results to modified gravity scenarios.

## Key findings

- Without backreaction, extremal and nearly extremal Kerr-MOG black holes can be overspun.
- Backreaction effects restore the validity of cosmic censorship and the third law for lpha0.03.
- The results include the Kerr black hole case (lpha=0).

## Abstract

We evaluate the validity of the weak form of the cosmic censorship conjecture and the third law of black hole dynamics for Kerr-MOG black holes interacting with scalar test fields. Ignoring backreaction effects, we first show that both extremal and nearly extremal Kerr-MOG black holes can be overspun into naked singularities by scalar test fields with a frequency slightly above the superradiance limit. In addition, nearly extremal Kerr-Mog black holes can be continuously driven to extremality by test fields. Next, we employ backreaction effects based on the argument that the angular velocity of the event horizon increases before the absorption of the test field. Incorporating the backreaction effects, we derive that the weak form of the cosmic censorship and the third law are both valid for Kerr-Mog black holes with a modification parameter $\alpha \lesssim 0.03$, which includes the Kerr case with $\alpha=0$.