Weak cosmic censorship conjecture is not violated for a rotating linear dilaton black hole

TL;DR

This paper demonstrates that the weak cosmic censorship conjecture remains valid for rotating linear dilaton black holes when considering second order effects, confirming the robustness of the conjecture through two different analytical methods.

Contribution

The study applies two methods to verify the weak cosmic censorship conjecture for rotating linear dilaton black holes, including second order modifications, showing the conjecture's validity.

Findings

Nearly extremal black holes can be overspun without second order effects.

Extremal black holes cannot be overspun, preserving the conjecture.

Second order modifications protect the weak cosmic censorship conjecture.

Abstract

In this paper, we investigate the validity of the weak cosmic censorship conjecture(WCCC) for a rotating linear dilaton black hole from two different methods. By using the classsical ingoing test particle method, we obtain the same results as given in the new version of gedanken experiment recently proposed by Wald. We find that even for this rotating linear dilaton black hole the Iyer-Wald formalism is still functioning. By comparing these two methods, we find that the same result will be obtained in both cases up to first order. The nearly extremal black hole can be overspun, while the extremal one cannot be overspun. When we include the second order modification into consideration, the Iyer-Wald method show that even for the nearly extremal black hole, the WCCC is well protected. These results imply that weak cosmic censorship conjecture is still valid using the ingoing test particle method up to second order modification.