Weak Cosmic Censorship Conjecture in Kerr-(Anti-)de Sitter Black Hole with Scalar Field

TL;DR

This paper tests the weak cosmic censorship conjecture in Kerr-(anti-)de Sitter black holes by analyzing scalar field scattering, demonstrating its validity across various initial states without relying on thermodynamic laws.

Contribution

It provides a novel proof of the conjecture's validity in all initial states of black holes using scalar field fluxes, differing from particle-based approaches.

Findings

The conjecture holds for all initial black hole states.

Scalar field fluxes transfer energy and angular momentum without violating the extremal condition.

The angular velocity approaches saturation over time during scalar field interaction.

Abstract

We investigate the weak cosmic censorship conjecture in Kerr-(anti-)de Sitter black holes under the scattering of a scalar field. We test the conjecture in terms of whether the black hole can exceed the extremal condition with respect to its change caused by the energy and angular momentum fluxes of the scalar field. Without imposing the laws of thermodynamics, we prove that the conjecture is valid in all the initial states of the black hole (non-extremal, near-extremal, and extremal black holes). The validity in the case of the near-extremal black hole is different from the results of similar tests conducted by adding a particle because the fluxes represent the energy and angular momentum transferred to the black hole during the time interval not included in the tests involving the particle. Using the time interval, we show that the angular velocity of the black hole with the scalar field of a constant state takes a long time for saturation to the frequency of the scalar field.