Test fields and naked singularities: is the second law the cosmic censor?

TL;DR

The paper addresses whether extremal or near-extremal Kerr-Newman black holes can be destroyed by classical test fields, clarifying that previous overspin results arise from a flawed energy-flux assumption that violates Hawking's area increase theorem. Through explicit near-horizon analyses, it shows that a test scalar field cannot overspin an extremal Kerr-Newman black hole because the horizon area does not decrease ($dA\ge 0$, with $\Delta'_{\min}\le 0$ for scalars). In contrast, a neutrino field with $\omega < m\Omega_H$ can decrease the horizon area ($dA<0$) and potentially destroy the horizon, highlighting a direct link between second-law violations and possible violations of weak cosmic censorship. The work thereby reinforces the thermodynamic underpinning of censorship for scalar perturbations while identifying a fermionic counterexample under certain conditions, and it discusses the broader implications for backreaction and the general relationship between black hole thermodynamics and cosmic censorship.

Abstract

It has been claimed that a Kerr-Newman black hole can generically be overspun by neutral test fields, and it has been argued that even when backreactions are taken into account, the black hole can still be destroyed. In this paper, we revisit the weak cosmic censorship conjecture for a Kerr-Newman black hole with a test scalar field and a neutrino field, and point out that the assumption in previous work regarding the energy and angular momentum of the test fields absorbed by the black hole violates the second law of black hole thermodynamics. By solving the test scalar field and neutrino field near the event horizon explicitly, we demonstrate that an extremal Kerr-Newman black hole cannot be overspun by a test scalar field but can be destroyed by a neutrino field. Our results indicate that the condition required to overspin an extremal Kerr-Newman black hole coincides with the condition needed to violate the second law of black hole thermodynamics. Furthermore, we observe that such a violation of the second law might inevitably result in a breakdown of the weak cosmic censorship conjecture.