The fate of strong cosmic censorship is ultimately linked to the extendibility of perturbation across the Cauchy Horizon and known to be violated in the near extremal region of a charged de Sitter black hole. Similar violations can also be realized in higher curvature theories, with the strength of violation becoming stronger as compared to general relativity. In this work, we extend this analysis further to study the validity of strong cosmic censorship conjecture in the context of the regularised four-dimensional Einstein Gauss-Bonnet theory with respect to both scalar and electromagnetic perturbation. We also study the late time tails of scalar fields.
We investigate the strong cosmic censorship conjecture in lukewarm Reissner-Nordström-de Sitter black holes (and Martínez-Troncoso-Zanelli black holes) using the quasinormal resonance of non-minimally coupled massive scalar field. The strong cosmic censorship conjecture is closely related to the stability of the Cauchy horizon governed by the decay rate of the dominant quasinormal mode. Here, dominant modes are obtained in the limits of small and large mass black holes. Then, we connect the modes by using the WKB approximation. In our analysis, the strong cosmic censorship conjecture is valid …
Hod's proposal claims that the least damped quasinormal mode of a black hole must have the imaginary part smaller than half of the surface gravity at the event horizon. The Strong Cosmic Censorship in General Relativity implies that this bound must be even weaker: half of the surface gravity at the Cauchy horizon. The appealing question is whether these bounds are limited by the Einstein theory only? Here we will present numerical evidence that once the black hole size is much smaller than then the radius of the cosmological horizon, both the Hod's proposal and the strong cosmic censorship bou…
The quasinormal resonant modes of massless neutral fields in near-extremal Kerr-Newman-de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime ${\bar a}> \sqrt{{1-2{\barΛ}\over{4+{\barΛ}/3}}}$, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula $\Imω(n)=κ_+\cdot(n+{1\over2})$ [here the physical parameters $\{{\bar a},κ_+,{\barΛ},n\}$ are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensio…
Recent work has argued that the strong cosmic censorship (SCC) conjecture is violated by near-extremal Reissner-Nordström de Sitter (RNdS) black holes but respected by Kerr-de Sitter black holes. It has also been shown that the conjecture is violated by near-extremal BTZ black holes. The latter result relies on a coincidence between "exterior" and "interior" quasinormal frequencies. If this coincidence were to occur also for RNdS or Kerr-dS then it would significantly modify the conclusions of earlier work. In this paper, it is demonstrated that this coincidence does not occur for RNdS or Kerr…
The fate of Cauchy horizons, such as those found inside charged black holes, is intrinsically connected to the decay of small perturbations exterior to the event horizon. As such, the validity of the strong cosmic censorship (SCC) conjecture is tied to how effectively the exterior damps fluctuations. Here, we study massless scalar fields in the exterior of Reissner--Nordstrom--de Sitter black holes. Their decay rates are governed by quasinormal modes of the black hole. We identify three families of modes in these spacetimes: one directly linked to the photon sphere, well described by standard …
Investigating the quasinormal modes of a massive scalar field on the 3-dimensional black string (3dBS), we study the strong cosmic censorship (SCC) conjecture for the 3dBS in the T-dual relationship with the 3-dimensional rotating anti-de-Sitter (BTZ) black hole. It is shown that even though geometries of the two spacetimes are quite different, such as asymptotically AdS for the BTZ black hole and asymptotically flat for the 3dBS, the BTZ black hole and the 3dBS share similar properties for the SCC. Concretely speaking, the SCC conjecture can be violated even for asymptotically flat spacetime,…
Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analys…
Two numerical methods are used to calculate quasinormal modes (QNMs) of near-extremal black holes/strings in the generalized spherically/cylindrically symmetric background, the Asymptotic Iteration Method (AIM) and the Spectral Method. The numerical results confirm the accuracy of the approximate analytic formula using the Pöschl-Teller potential. Our analytic formula is used to investigate the Strong Cosmic Censorship conjecture of extremal and near-extremal black holes in Ref. \cite{Burikham:2020dfi}.
We investigate the instability of the unstable circular orbit of a charged null particle to test the strong cosmic censorship conjecture in Nariai-type near-extremal Reissner--Nordström--de Sitter black holes. The instability is estimated as the Lyapunov exponent and found to depend on the mass and charge of the black hole. Then, we explicitly show that charged null particles in unstable circular orbits correspond to the charged massless scalar field in the eikonal limit. This provides a compact relationship representing the quasinormal frequency in terms of the characteristics of unstable cir…
We present a plausible counterexample to the weak cosmic censorship conjecture in the four-dimensional Einstein-Scalar theory with asymptotically flat boundary conditions. Our setup stems from the analysis of the massive Klein-Gordon equation on a fixed Kerr black hole background. In particular, we construct the quasinormal spectrum numerically, and analytically in the WKB approximation, then go on to compute its backreaction on the Kerr geometry. In the regime of parameters where the analytic and numerical techniques overlap we find perfect agreement. We give strong evidence for the existence…
Spin-($0$, $1$, $\frac{1}{2}$) Field Perturbations, Quasinormal Modes, Overtones, Greybody Factors and Strong Cosmic Censorship of Einstein-Skyrme Black Holes
The Assam Royal Global University（阿萨姆皇家全球大学）；Al-Hussein Bin Talal University（侯赛因·本·塔拉勒大学）；Eastern Mediterranean University（东地中海大学）
Rotating and/or charged black hole spacetimes possess a Cauchy horizon, beyond which Einstein's equations of General Relativity cease to be deterministic. This led to the formulation of the Strong Cosmic Censorship conjecture that such horizons become irregular under field perturbations. We consider linear field perturbations of rotating and electrically-charged (Kerr-Newman-de Sitter) black holes in a universe with a positive cosmological constant. By calculating the quasinormal modes for scalar and fermion fields, we provide evidence for the existence of weak solutions to Einstein's equation…
We study the phenomena of mass inflation using the Ori model for a rotating BTZ black hole that is sufficiently far from extremality, and show that the right Cauchy horizon ($\mathcal{CH}^+_R$) of the BTZ black hole becomes singular. Motivated by the recent analysis of Dias, Reall, Santos [J. High Energy Phys. 12 (2019) 097], we choose the retrograde quasinormal modes to govern the decay of perturbations exterior to the black hole. The resulting model captures the violation of the strong cosmic censorship conjecture near extremality. On the other hand, far from extremality, the $\mathcal{CH}^+…
We study the holographic duals of bosonic and fermionic fields and compute their Quasinormal Frequencies (QNF) by exploiting that they are massive charged fields in $\mathrm{AdS_2 \times \mathcal{K}}$. In particular, we assess the stability of the scalar and fermionic operators in Myers-Perry's black holes with equal angular momenta. We compute the central charge and the Hawking-entropy and introduce extremality parameters to determine the properties of the dual CFT. Then, we briefly discuss how detection of Spin-2 fields can pave the way for more deep understanding of the holographic principl…
The strong cosmic censorship conjecture states (SCCC) that one cannot extend spacetime beyond the Cauchy horizon with a square-integrable connection. This conjecture was postulated to save the deterministic nature of the most successful theory of gravitation, general relativity. In order to explore the validation/violation of the SCCC for the charged anti-de Sitter black hole spacetime, we compute the ratio of the imaginary part of the quasinormal mode frequencies and the surface gravity at the Cauchy horizon both analytically and numerically. The lowest value of which defines the key paramete…
A number of near-extremal conditions are utilized to simplify the equation of motion of the neutral scalar perturbations in generalized spherically symmetric black hole background into a differential equation with the Pöschl-Teller potential. An analytic formula for quasinormal frequencies is obtained. The analytic formula is then used to investigate Strong Cosmic Censorship conjectures~(SCC) of the generalized black hole spacetime for the smooth initial data. The Christodoulou version of the SCC is found to be violated for certain regions of the black hole parameter space including the black …
We study linear scalar perturbations of black holes in two-dimensional (2D) gravity models with a particular emphasis on Jackiw-Teitelboim (JT) gravity. We obtain an exact expression of the quasinormal mode frequencies for single horizon black holes in JT gravity and then verify it numerically using the Horowitz-Hubeny method. For a 2D Reissner-Nordström like solution, we find that the massless scalar wave equation reduces to the confluent Heun equation using which we calculate the Hawking spectra. Finally, we consider the dimensionally reduced Bañados-Teitelboim-Zanelli (BTZ) black hole and o…
It has been shown that the quasinormal modes of perturebated fields can be used to investigate the validity of strong cosmic censorship (SCC). Relevant issues for Reissner-Nordstrom-de Sitter (RNdS) black holes and Born-Infeld-de Sitter (BI-dS) black holes have been discussed. In this paper, we investigate SCC in an asymptotic RN-dS black hole with logarithmic nonlinear electromagnetic field perturbed by massless scalar fields. It has been argued that SCC can be violated in a near-extremal RN-dS black hole. However, we find that the NLED effect can rescue SCC for a near-extremal logarithmic-de…
It is proved that dynamically formed Reissner-Nordström-de Sitter (RNdS) black holes, which have recently been claimed to provide counter-examples to the Penrose strong cosmic censorship conjecture, are characterized by unstable (singular) inner Cauchy horizons. The proof is based on analytical techniques which explicitly reveal the fact that {\it charged} massive scalar fields in the charged RNdS black-hole spacetime are characterized, in the large-coupling regime, by quasinormal resonant frequencies with $\Imω^{\text{min}}<{1\over2}κ_+$, where $κ_+$ is the surface gravity of the black-hole e…
Recently, it is found that the strong cosmic censorship (SCC) is violated in RNdS black hole by a minimal coupled neutral massless scalar field at the linear perturbation level. For the Einstein-Maxwell-Scalar-Gauss-Bonnet theory which is famous for the spontaneous scalarization phenomenon, there exists the scalar field coupled with the Gauss-Bonnet term. Whether the SCC of the RNdS black hole can be repaired by the non-minimal coupled scalar field perturbation at the linear level becomes an interesting question. In this paper, we firstly investigate the extendibility of the metric beyond the …
It has been established that Christodoulou's formulation of Strong Cosmic Censorship (SCC) is violated by Reissner-Nordström-de Sitter black holes, but holds in four-dimensional Kerr-de Sitter black holes. We show that SCC is also respected by equal angular momenta (cohomogeneity-1) Myers-Perry-de Sitter (MP-dS) in odd $d \ge 5$ spacetime dimensions. This suggests that the preservation of SCC in rotating backgrounds might be a universal property of Einstein gravity and not limited to the d = 4 Kerr-dS background. As required to discuss SCC in de Sitter spacetimes, we also study important aspec…
We clarify a number of issues that arise when extending the analysis of Strong Cosmic Censorship (SCC) to perturbations of highly charged Reissner-Nordström de Sitter (RNdS) spacetimes. The linear stability of the Cauchy horizon can be determined from the spectral gap of quasinormal modes, thus giving a clear idea of the ranges of parameters that are likely to lead to SCC violations for infinitesimally small perturbations. However, the situation becomes much more subtle once nonlinear backreaction is taken into account. These subtleties have created a considerable amount of confusion in the li…
Scalar perturbations and strong cosmic censorship in a regular ABGB-de Sitter black hole spacetime
College of Physics and Materials Science, Tianjin Normal University（天津师范大学物理与材料科学学院）；Kavli Institute for Astronomy and Astrophysics, Peking University（北京大学科维理天文与天体物理研究所）
