Sitter Black Hole Research Articles

Appearance of de Sitter black holes and strong cosmic censorship

Appearance of de Sitter black holes and strong cosmic censorship

Bound on Lyapunov exponent in Kerr-Newman-de Sitter black holes by a charged particle

We investigate the bound on the Lyapunov exponents by a charged particle in Kerr-Newman-de Sitter black holes using analytic and numerical methods. We determine whether the Lyapunov exponent can exceed the bound by an electrically charged particle with an angular momentum. Our tests are applied to the de Sitter spacetime by the positive cosmological constant such as Reissner-Nordström-de Sitter, Kerr-de Sitter, and Kerr-Newman-de Sitter black holes. In particular, we consider Nariai and ultracold limits on these black holes for our tests. From our analysis results, there remain violations on the bound under the positive cosmological constant, and electric charge and angular momentum of the particle significantly impact the Lyapunov exponent.

Phase structures and critical behavior of rational non-linear electrodynamics Anti de Sitter black holes in Rastall gravity

This research paper presents a black hole solution with a rational nonlinear electrodynamics source within the Rastall gravity framework. The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior. The phase structure is examined using the extended first law of thermodynamics, with the cosmological constant Λ serving as pressure P. The isotherms exhibit van der Waals behavior at small values of horizon r +. The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the re-entrant phase transition occurs and disappears. We also explore the prevalent microstructure of black holes in Ruppeiner geometry, uncovering significant deviations in the nature of particle interactions from conventional practice. Moreover, the thermodynamic geometry is analyzed using the Ruppeiner formalism, with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity, and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar. The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures. Thus, there is an absolute correspondence.

Infinite Quantum Twisting at the Cauchy Horizon of Rotating Black Holes.

We present a numerical calculation of the expectation value of the quantum angular-momentum current flux density for a scalar field in the Unruh state near the inner horizon of a Kerr-de Sitter black hole. Our results indicate that this flux diverges as V_{-}^{-1} in a suitable Kruskal coordinate such that V_{-}=0 at the inner horizon. Depending on the parameter values of the scalar field and black hole that we consider, and depending on the polar angle (latitude), this flux can have different signs. In the near extremal cases considered, the angle average of the expectation value of the quantum angular momentum current flux is of the opposite sign as the angular momentum of the background itself, suggesting that, in the cases considered, quantum effects tend to decrease the total angular momentum of the spheres away from the extremal value. We also numerically calculate the energy flux component, which provides the leading order divergence of the quantum stress energy tensor, dominant over the classical stress energy tensor, at the inner horizon. Taking our expectation value of the quantum stress tensor as the source in the semiclassical Einstein equation, our analysis suggests that the spheres approaching the inner horizon can undergo an infinite twisting due to quantum effects along latitudes separating regions of infinite expansion and contraction.

Universality on thermodynamic relation with corrections in de Sitter black holes

We herein investigate the universal relation proposed by Goon and Penco in de Sitter black holes with electric charge or angular momentum. Our analysis focuses on the cosmological horizon, which only exists in de Sitter and Nariai spacetimes. Because the relation is given in a general case, the overall relationship may be valid. However, we elucidate the details of the relation, highlighting distinctions from those of (anti-)de Sitter black holes while affirming the validity of the relation. Furthermore, based on our analysis of Schwarzschild-de Sitter, Reissner-Nordström-de Sitter, and Kerr-de Sitter black holes, we demonstrate the universality of the thermodynamic relation in de Sitter black holes.

Critical behavior and Joule-Thomson expansion of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state* *Supported by the Doctoral Foundation of Zunyi Normal University of China (BS [2022]07, QJJ-[2022]-314), and the National Natural Science Foundation of China (12265007, 12264061). The research partially was supported by the Long-Term Conceptual Development of a University of Hradec Králové

By considering the concept of a unified single fluid model, referred to as modified Chaplygin gas (MCG), which amalgamates dark energy and dark matter, we explore the thermodynamic characteristics of charged anti-de Sitter (AdS) black holes existing in an unconventional fluid accompanied by MCG. To accomplish this objective, we derive the equations of state by regarding the charge as a thermodynamic variable. The effects of MCG parameters on the critical thermodynamic quantities ( , , ) are examined, followed by a detailed analysis of the diagram. To provide a clearer explanation of the phase transition, we present an analysis of the Gibbs free energy. It is important to note that if the Hawking temperature exceeds the critical temperature, a distinct pattern is observed known as swallowtail behavior. This indicates that the system undergoes a first-order phase transition from a smaller black hole to a larger one. The critical exponent of the system is found to be in complete agreement with that of the van der Waals fluid system. Furthermore, we investigate the impact of MCG parameters and black hole charge on Joule-Thomson (J-T) expansion in the extended phase space. The J-T coefficient is examined to pinpoint the exact region experiencing cooling or heating, and the observation reveals that the presence of negative heat capacity results in the occurrence of a cooling process. The impact of MCG on the inversion curve of charged black holes exhibits a striking resemblance to that observed in most multi-dimensional black hole systems. In addition, it is worth noting that certain parameters exert a significant influence on the ratio . For specific values of the MCG parameters, the ratio is consistent with the charged AdS black hole. The parameters γ and β have a non-negligible effect on the isenthalpic curve.

C=Anything and the switchback effect in Schwarzschild-de Sitter space

We investigate observables within the framework of the codimension-one C=Anything (CAny) proposal for Schwarzschild-de Sitter (SdS) space under the influence of shockwave sources. Within the proposal, there is a set of time-reversal invariant observables that display the same rate of growth at early and late times for a background with or without shockwave sources. Once we introduce shockwaves in the weak gravitational coupling regime, there is a decrease in the late-time complexity growth due to cancellations with early-time perturbations, known as the switchback effect. The result shows that some CAny observables in SdS may reproduce the same type of behavior found in anti-de Sitter black holes. We comment on how our results might guide us to new explorations in the putative quantum mechanical theory.

Constrained spin systems and KNdS black holes

Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure that involves multiple horizons, and so differs in key respects from asymptotically flat or AdS black holes. In this paper, we show that certain features of KNdS spacetimes can be reproduced by a constrained system of N non-interacting spins in a magnetic field. Both the KNdS and spin systems have bounded energy and entropy, a maximum of the entropy in the interior of the energy range, and a symmetry that maps lower energy states to higher energy states with the same entropy. Consequently, both systems have a temperature that can be positive or negative, where the gravitational temperature is defined analogously to that of the spins. We find that the number of spins N corresponds to 1/Λ for black holes with very small charge q and rotation parameter a, and scales like a2+q2/Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{\\left({a}^2+{q}^2\\right)/\\Lambda} $$\\end{document} for larger values of a and q. These comparisons show that certain key features of the complex thermodynamics of KNdS spacetimes are reproduced by a simple system of noninteracting spins, suggesting that there may be a relatively simple effective description of quantum de Sitter black holes in terms of a finite dimensional Hilbert space.

Scalar quasi-normal modes of accelerating Kerr-Newman-AdS black holes

We study linear scalar perturbations of slowly accelerating Kerr-Newman-anti-de Sitter black holes using the method of isomonodromic deformations. The conformally coupled Klein-Gordon equation separates into two second-order ordinary differential equations with five singularities. Nevertheless, the angular equation can be transformed into a Heun equation, for which we provide an asymptotic expansion for the angular eigenvalues in the small acceleration and rotation limit. In the radial case, we recast the boundary value problem in terms of a set of initial conditions for the isomonodromic tau function of Fuchsian systems with five regular singular points. For the sake of illustration, we compute the quasi-normal modes frequencies.

Dual CFT on Nariai limit for Kerr–Sen–dS black holes

In this work, we study the Kerr–Sen–de Sitter black hole (BH) in the Nariai limit where the event and cosmological horizon coincide. We show that the near-horizon Kerr–Sen–de Sitter black hole in Nariai limit is a fiber over AdS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document} with an appropriate coordinate transformation, instead of fiber over dS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$_2$$\\end{document}. Hence, we can compute the associated central charge and CFT temperature by using the Kerr/CFT method. It is remarkably exhibited that through Cardy’s growth of states, the Bekenstein–Hawking entropy on cosmological horizon is reproduced. Moreover, we show that the radial equation of the quantum scalar field in J- and Q-pictures on this charged rotating background in Nariai limit can be portrayed in quadratic Casimir operator form with SL(2,R)×SL(2,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SL(2,R)\ imes SL(2,R)$$\\end{document} isometry. We also compute the corresponding thermodynamic quantities from CFT to find the absorption cross-section and real-time correlator in J-picture. In Q-picture, we do not find a well-defined CFT description. We then extend the study of quantum scalar field in Nariai limit for Kerr–Newman–dS black hole solution and show that the hidden conformal symmetry on this black hole’s background in J- and Q-pictures is well-defined.

Investigation of black hole complementarity in AdS2 black holes

Black hole complementarity plays a pivotal role in resolving the information loss paradox by treating Hawking radiation as carriers of information, apart from the complicated mechanisms involved in decoding information from this radiation. The thought experiment proposed by Susskind and Thorlacius, as well as the criteria set forth by Hayden and Preskill, provide deep insights into the intricate relationship of black hole complementarity between fiducial and infalling observers. We execute the Alice-Bob thought experiment in the context of two-dimensional anti-de Sitter black holes. It turns out that information cloning can be avoided in the case of a large black hole. According to the Hayden-Preskill criteria, if the scale parameter associated with the explicit breaking of the one-dimensional group of reparametrizations is significantly exceed the squared mass of the black hole, then information cloning can be effectively evaded.

De Sitter space is sometimes not empty

Multiple lines of evidence suggest that the Hilbert space of an isolated de Sitter universe is one dimensional but can appear larger when probed by a gravitating observer. To test this idea, we compute the von Neumann entropy of a field theory in a two-dimensional de Sitter universe which is entangled in a thermal-like state with the same field theory on a disjoint, asymptotically anti-de Sitter (AdS) black hole. Previously, it was shown that the replica trick for computing the entropy of such entangled gravitating systems requires the inclusion of a non-perturbative effect in quantum gravity — novel wormholes connecting the two spaces. Here we show that: (a) the expected wormholes connecting de Sitter and AdS universes exist, avoiding a no-go theorem via the presence of sources on the AdS boundary; (b) the entanglement entropy vanishes if the nominal entropy of the de Sitter cosmological horizon SdS=AhorizondS/4GN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left({S}_{\ extrm{dS}}={A}_{\ extrm{horizon}}^{\ extrm{dS}}/4{G}_{\ extrm{N}}\\right) $$\\end{document} is less than the entropy of the AdS black hole horizon SBH=AhorizonAdS/4GN\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\left({S}_{\ extrm{BH}}={A}_{\ extrm{horizon}}^{\ extrm{AdS}}/4{G}_{\ extrm{N}}\\right) $$\\end{document}, i.e., SdS< SBH; (c) the entanglement entropy is finite when SdS > SBH. Thus, the de Sitter Hilbert space is effectively nontrivial only when SdS > SBH. The AdS black hole we introduce can be regarded as an “observer” for de Sitter space. In this sense, our result is a non-perturbative generalization of the recent perturbative argument that the algebra of observables on the de Sitter static patch becomes nontrivial in the presence of an observer.

Quasinormal modes of C-metric from SCFTs

We study the quasinormal modes (QNM) of the charged C-metric, which physically stands for a charged accelerating black hole, with the help of Nekrasov’s partition function of 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 superconformal field theories (SCFTs). The QNM in the charged C-metric are classified into three types: the photon-surface modes, the accelerating modes and the near-extremal modes, and it is curious how the single quantization condition proposed in [1] can reproduce all the different families. We show that the connection formula encoded in terms of Nekrasov’s partition function captures all these families of QNM numerically and recovers the asymptotic behavior of the accelerating and the near-extremal modes analytically. Using the connection formulae of different 4d N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 2 SCFTs, one can solve both the radial and the angular parts of the scalar perturbation equation respectively. The same algorithm can be applied to the de Sitter (dS) black holes to calculate both the dS modes and the photon-sphere modes.

No scalar-haired Cauchy horizon theorem in charged Gauss–Bonnet black holes

Recently, a “no inner (Cauchy) horizon theorem” for static black holes with non-trivial scalar hairs has been proved in Einstein–Maxwell–scalar theories and also in Einstein–Maxwell–Horndeski theories with the non-minimal coupling of a charged (complex) scalar field to Einstein tensor. In this paper, we study an extension of the theorem to the static black holes in Einstein–Maxwell–Gauss–Bonnet-scalar theories, or simply, charged Gauss–Bonnet (GB) black holes. We find that no inner horizon with charged scalar hairs is allowed for the planar (k=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=0$$\\end{document}) black holes, as in the case without GB term. On the other hand, for the non-planar (k=±1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k=\\pm 1$$\\end{document}) black holes, we find that the haired inner horizon can not be excluded due to GB effect generally, though we can not find a simple condition for its existence. As some explicit examples of the theorem, we study numerical GB black hole solutions with charged scalar hairs and Cauchy horizons in asymptotically anti-de Sitter space, and find good agreements with the theorem. Additionally, in an Appendix, we prove a “no-go theorem” for charged de Sitter black holes (with or without GB terms) with charged scalar hairs in arbitrary dimensions.

Quasinormal Modes and Greybody Factors of de Sitter Black Holes Surrounded by Quintessence in Rastall Gravity

AbstractIn this work, the quasinormal mode, greybody factors, and absorption cross section of de Sitter Reissner‐Nordström black hole surrounded by quintessence field in Rastall gravity are studied. The violation of energy‐momentum conservation has a non‐linear effect on the quasinormal modes. With an increase in the black hole charge, both real parts of quasinormal modes i.e. oscillation frequency of ring‐down Gravitational Waves (GWs) and damping or decay rate of GWs increase non‐linearly. A similar observation is made for the black hole structural parameter also, however in this case the variation is almost linear. The remnant mass of a black hole depends on different physical parameters of a black hole. In the case of greybody factors also, both parameters have similar impacts are observed. With an increase in these parameters, greybody factors decrease. Moreover, the null geodesics and the impact of Rastall gravity on the light trajectory are also investigated. Our study suggests that the presence of a surrounding quintessence field may shadow the existence of black hole charges in such black hole configurations.

Quasinormal modes and isospectrality of Bardeen (Anti-) de Sitter black holes* *Supported by the the Natural Science Foundation of Hunan Province, China (2022JJ40262), and the National Natural Science Foundation of China (12375046, 12205254)

Black holes (BHs) exhibiting coordinate singularities but lacking essential singularities throughout the spacetime are referred to as regular black holes (RBHs). The initial formulation of RBHs was presented by Bardeen, who considered the Einstein equation coupled with a nonlinear electromagnetic field. In this study, we investigate the gravitational perturbations, including the axial and polar sectors, of the Bardeen (Anti-) de Sitter black holes. We derive the master equations with source terms for both axial and polar perturbations and subsequently compute the quasinormal modes (QNMs) through numerical methods. For the Bardeen de Sitter black hole, we employ the 6th-order WKB approach. The numerical results reveal that the isospectrality is broken in this case. Conversely, the QNM frequencies are calculated using the HH method for the Bardeen Anti-de Sitter black hole.

Quasilinear wave equations on Schwarzschild–de Sitter

We give an elementary new argument for global existence and exponential decay of solutions of quasilinear wave equations on Schwarzschild–de Sitter black hole backgrounds, for appropriately small initial data. The core of the argument is entirely local, based on time translation invariant energy estimates in spacetime slabs of fixed time length. Global existence then follows simply by iterating this local result in consecutive spacetime slabs. We infer that an appropriate future energy flux decays exponentially with respect to the energy flux of the initial data.

P-v criticality of charged Reissner–Nordström-de Sitter black hole under the influence of Lorentz violation theory

In this paper, the modified Hawking radiation and the P-v criticality of Reissner–Nordström-de Sitter (RNdS) black hole are investigated by using Dirac equation with Lorentz violation theory in curved space–time. Taking cosmological constant as the thermodynamic pressure and its conjugate quantity as thermodynamic volume, the analogy between the RNdS black hole in the ensemble with fixed charge and van der Waals liquid-gas system is derived. We also study the equation of state, critical exponents, critical point, heat capacity, entropy correction, Gibbs free energy. It is worth mentioning that the critical temperature, entropy, Gibbs free energy and Helmholtz free energy are modified but the critical exponents are found to be unchanged due to the influence of Lorentz violation theory. We observe that the number of Hawking–Page critical point increases due to Lorentz violation theory.

Overcharging an accelerating Reissner-Nordström-anti-de Sitter black hole with test field and particle

Accelerating black holes have been widely studied in the context of black hole thermodynamics, holographic gravity theories, and in the description of black holes at the center of galaxies. As a fundamental assumption to ensure spacetime causality, we investigate the weak cosmic censorship conjecture (WCCC) in the accelerating Reissner-Nordström-Anti-de Sitter (RN-AdS) spacetime through the scattering of a charged field and the absorption of a charged particle. For the scattering of a charged scalar field, both near-extremal and extremal accelerating RN-AdS black holes cannot be overcharged, thereby upholding the validity of the WCCC. In the case of the absorption of a test charged particle, the results demonstrate that the event horizon of the extremal accelerating RN-AdS black hole cannot be destroyed, while the event horizon of the near-extremal black hole can be overcharged if the test particle satisfies certain conditions. The above results suggest that, in the case of test particles, second-order effects like self-force and self-energy should be further considered.

Ruppeiner geometry and the fluctuation of the RN-AdS black hole in framework of the extensive thermodynamics

In this study, the Ruppeiner geometry and fluctuations of a four-dimensional charged Anti-de Sitter (AdS) black hole within the context of extensive thermodynamics have been investigated. By fixing the AdS radius in Vissers' construction, an extensive thermodynamics description of the RN-AdS black hole is established, with the central charge playing the role of the particle number, introducing the concept of a subsystem into black hole thermodynamics. By employing the density of thermodynamic variables, the phase transition of the black hole is reexamined, and this result holds for black holes with different AdS backgrounds. Furthermore, the authors delve into a detailed analysis of the Ruppeiner geometry using fluctuation theory. Interestingly, an increase in the particle number of the smaller subsystem is found to induce a reduction in the thermodynamic curvature scalar.