Investigating the gedanken experiment to destroy the event horizon of a regular black hole

Understand

Recently, Li and Bambi proposed a hypothesis that the event horizon of a regular black hole can be destroyed because these objects have no gravitational singularity and therefore they are not protected by the weak cosmic censorship conjecture (WCCC).

• In this paper, to test their hypothesis, we perform the new version of the gedanken experiments proposed by Sorce and Wald to overcharge a near extremal static electrically regular black hole.
• After introducing the stability condition of the spacetime and the null energy condition of matter fields, we derive the first-order and second-order perturbation inequalities of the perturbation matter fields based on the Iyer-Wald formalism.
• As a result, we find that these regular black holes cannot be destroyed under the second-order approximation after these two perturbation inequalities are taken into account, even though they are not protected by the WCCC.