Abstract
The new version of the gedanken experiment proposed by Sorce and Wald has been used to examine the weak cosmic censorship conjecture (WCCC) for black holes at the second-order approximation of the matter fields perturbation. However, only considering the perturbation until the second-order approximation is incomplete because there is an optimal option such that the existing condition of the event horizon vanishes at second- order. For this circumstance, we cannot judge whether the WCCC is satisfied at this order. In our investigation, the kth-order perturbation inequality is generally derived. Using the inequalities, we examine the WCCC for nearly extremal Reissner-Nordstöm black holes at higher-order approximation. It is shown that the WCCC cannot be violated yet after the perturbation. From this result, it can be indicated that the WCCC is strictly satisfied at the perturbation level for nearly extremal RN black holes.
Highlights
JHEP05(2020)161 fields at first- and second-order approximations
The new version of the gedanken experiment proposed by Sorce and Wald has been used to examine the weak cosmic censorship conjecture (WCCC) for black holes at the second-order approximation of the matter fields perturbation
It can be indicated that the WCCC is strictly satisfied at the perturbation level for nearly extremal RN black holes
Summary
For the four-dimensional Einstein-Maxwell gravitational theory, the Lagrangian is given as. When the extra matter fields vanish, a class of static spherically symmetric solutions describing RN spacetimes in Eddington-Finkelstein coordinates is given as ds2 = −f (r)dv2 + 2dvdr + r2 dθ2 + sin θdφ , Q. The stability condition states at sufficiently late times (where the perturbation matter fields all pass through the event horizon), the spacetime geometry can be described by the class of static spherically symmetric solutions of the RN spacetime. It means that at sufficiently late times, eq (2.3) can be used to describe the spacetime geometry, just the parameters M and Q in the line element are replaced to M (λ) and
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