† Corresponding author. E-mail:
Supported by the National Science Foundation of China under Grant Nos. 11675139, 11405130, 11647050
If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr-Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed parameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime.
According to the so-called cosmic censorship conjecture,[1] all physical singularities due to gravitational collapse should be hidden behind an event horizon. This hypothesis that no naked singularity occurs in our universe can be described in weak and strong versions.[2] One way of testing the week cosmic censorship conjecture (WCCC) is to throw a test particle into an existing black hole. If the particle can pass through the horizon and change the parameters of the black hole so that the horizon disappears, then the cosmic censorship conjecture might break down.
The seminal work was done by Wald,[3] which showed that a test particle can not destroy the horizon of an extremal Kerr-Newman black hole. From then on, many authors followed the spirit of Wald’s gadanken experiment and revisited the problem of WCC violation. Some of the attempts involving test particles have been successful to produce naked singularities.[4–8] For example, Jacobson et al.[4] asserted that it would be possible to destroy a Kerr black hole with infalling test particle if we start with a near-extremal configuration, rather than an extremal black hole. In Ref. [5], Hubeny showed that overcharging a near-extremal Reissner-Nordstrom (RN) black hole is possible by injecting a test particle into the black hole. For charged and spinning black holes, it is possible to destroy an extremal[9] and near-extremal[10] Kerr-Newman black hole by a test particle with electric charge and angular momentum by neglecting the backreaction effect. The issue about the problem of cosmic censorship has been extensively studied in recent years.[11–19]
Since the discovery of the AdS/CFT correspondence,[20–22] its developments have brought about many new insights into the nature of black holes. The study of asymptotically anti-de Sitter black holes has become more important and realistic than ever. It is interesting to know the role of Λ in the discussing turning a black hole into a naked singularity by plugging a test particle into black hole. Recently, Zhang et al.[23] asserted that an extremal Reissner-Nordström anti-de Sitter black hole can be overcharged by a test particle and both extremal Kerrde-Sitter/anti-de-Sitter black holes can be overspun by a test particle, which implies a possible breakdown of the cosmic censorship conjecture. Moreover, we have also recovered that a test particle may destroy the horizon of an extremal Kerr-Newman-AdS black hole, resulting in an apparent violation of the cosmic censorship.[24] In this paper, we further study the near-extremal Kerr-Newman-AdS black holes, and will find that the possibility to destroy a near-extremal Kerr-Newman-AdS by plunging test particles across their event horizon when neglecting the self-force, self-energy, and radiative effects. We also provide a numerical plot showing that a test particle, which potentially could destroy the black hole, could really fall all the way from infinity into the black hole.
In Sec.
In four-dimensional spacetime, the Kerr-Newman-AdS metric takes the following form in Boyer-Lindquist-type coordinates[24–25]
Now let us consider a test particle with electric charge q, energy E, and orbital angular L moves along a geodesic in a Kerr-Newman-AdS spacetime, the conserved energy of the test particle is described as[24,27]
To investigate the range of energy ΔE, we chose the parameters Q = 23.217 58, a = 0.1, q = 0.1, L = 0.1, then the radius of extremal black hole is 3.638 34 and mass M is 100. By choosing the values of δ, we can get the corresponding values of Emax by solving Eq. (
In order to get the minimum energy for the particle to reach the event horizon, we can rewrite Eq. (
Based on Eqs. (
From Eq. (
From Fig.
Next, we will show that a particle from infinity whose energy between Emax and Emin could really fall into the black hole. Since the metric is axisymmetric, the test particle can fall along the orbit which lying entirely in the plane θ = π/2. For such an orbit, one can solve Eq. (
Figure
In this paper, we have found that a test particle may destroy the horizon of a near-extremal Kerr-Newman-AdS black hole, resulting in an apparent violation of the cosmic censorship without taking into account the radiative and self-force effects. Moreover, the allowed range for the particle’s energy E to destroy the black hole is narrow, which indicates that the energy of the particle must be finely tuned. Generally, it regards that taking the radiative and self-force effects[28–30] into account could compensate for the WCC violations.
It is worth to point out that in Refs. [9–10, 27], the higher order term in evaluating the allowed upper limit of particle’s energy Emax is neglected. While in our paper, we sacrifice the analyticity of Emax and use the numerical method, so we can plot the allowed range for test particle’s energy to destroy the Kerr-Newman-AdS black hole without approximation. Figure
Nevertheless, the analysis performed in this paper neglects the radiative and self-force effects. The fact that ΔE is very small leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime. We will address these projects in our future work.
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