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Register a new userWeak cosmic censorship conjecture in BTZ black holes with scalar fields
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Deyou Chen
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The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested by the test particles and fields. It was claimed that this black hole could be overspun. In this paper, we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes by the scattering of the scalar field. The first law of thermodynamics in the non-extremal BTZ black hole is recovered. For the extremal and near-extremal black holes, due to the divergence of the variation of the entropy, we test the weak cosmic censorship conjecture by evaluating the minimum values of the function $f$. Both of the extremal and near-extremal black holes cannot be overspun.
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It has been shown recently that the strong cosmic censorship conjecture is violated by near-extremal Reissner-Nordstrom-de Sitter black holes. We investigate whether the introduction of a charged scalar field can rescue strong cosmic censorship. We find that such a field improves the situation but there is always a neighbourhood of extremality in which strong cosmic censorship is violated by perturbations arising from smooth initial data.
By throwing a test charged particle into a Reissner-Nordstrom (RN) black hole, we test the validity of the first and second laws of thermodynamics and weak cosmic censorship conjecture (WCCC) with two types of boundary conditions, i.e., the asymptotically anti-de Sitter (AdS) space and a Dirichlet cavity wall placed in the asymptotically at space. For the RN-AdS black hole, the second law of thermodynamics is satisfied, and the WCCC is violated for both extremal and nearextremal black holes. For the RN black hole in a cavity, the entropy can either increase or decrease depending on the change in the charge, and WCCC is satisfied/violated for the extremal/nearextremal black hole. Our results indicate that there may be a connection between the black hole thermodynamics and the boundary condition imposed on the black hole.
Treating the cosmological constant as a dynamical variable, we investigate the thermodynamics and weak cosmic censorship conjecture (WCCC) of a charged AdS black hole (BH) in the Rastall gravity. We determine the energy momentum relation of charged fermion at the horizon of the BH by using the Dirac equation. Based on this relation, we show that the first law of thermodynamics (FLT) still holds as a fermion is absorbed by the BH. However, the entropy of both the extremal and near-extremal BH decreases in the irreversible process, which means that the second law of thermodynamics (SLT) is violated. Furthermore, we verify the validity of the WCCC by the minimum values of the metric function h(r) at its final state. For the extremal charged AdS BH in the Rastall gravity, we find that the WCCC is valid always since the BH is extreme. While for the case of near-extremal BH, we find the WCCC could be violable in the extended phase space (EPS), depending on the value of the parameters of the BH and their variations.
In the framework of the new version of the gedanken experiments proposed by Sorce and Wald, we investigate the weak cosmic censorship conjecture (WCCC) for an Einstein-Maxwell-Dilaton-Axion (EMDA) black hole. Our result shows that no violations of WCCC can occur with the increase of the background solution parameters for this near-extremal EMDA black hole when the second order correction of the perturbations is taken into account. Namely, the near-extremal EMDA black hole cannot be over-charged or over-spun.
The thermodynamics and weak cosmic censorship conjecture in Reissner-Nordstr$ddot{o}$m anti-de Sitter black holes are investigated by the scattering of the scalar field. The first law of thermodynamics in the non-extremal Reissner-Nordstr$ddot{o}$m anti-de Sitter black hole is recovered by the scattering. The increase of the horizon radius indicates that the singularity is not naked in this black hole. For the near-extremal and extremal black holes, the validity is tested by the minimum values of the function $f$ at their final states. It is found that both of the near-extremal and extremal black holes can not be overcharged. When $omega=qphi$, the final state of the extremal black hole is still an extremal black hole. When $omega eq qphi$, it becomes a near-extremal black hole with new mass and charge.
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