De Sitter Black Hole Research Articles

Review of weak cosmic censorship conjecture in black hole with particle absorption

In this review, we briefly introduce particle absorption as an approach for investigating the weak cosmic censorship conjecture with regard to Kerr-(anti-)de Sitter black holes as the simplest example. The conjecture can be tested by determining whether the horizon of a black hole is stable under a perturbation. Here, we consider the perturbation from an ingoing particle to the black hole. Through particle absorption, we can demonstrate the first order of changes in a black hole. Hence, this analysis provides the most important term in the changes. Furthermore, the changes in black holes are consistent with the laws of thermodynamics.

Entropic force between two horizons of dilaton black holes with a power-Maxwell field * *Supported by the National Natural Science Foundation of China (11705107, 11847123, 11475108, 11705106, 11605107), the Natural Science Foundation of Shanxi Province, China (201601D102004), the Scientific and Technological Innovation Programs of Higher Education Institutions of Shanxi Province, China (2019L0743, 2020L0471, 2020L0472)

In this paper, we consider -dimensional topological dilaton de Sitter black holes with a power-Maxwell field as thermodynamic systems. The thermodynamic quantities corresponding to the black hole horizon and the cosmological horizon are interrelated. Therefore, the total entropy of the space-time should be the sum of the entropies of the black hole horizon and the cosmological horizon plus a correction term which is produced by the association of the two horizons. We analyze the entropic force produced by the correction term at given temperatures, which is affected by the parameters and dimensions of the space-time. It is shown that the change of entropic force with the position ratio of the two horizons in some regions is similar to that of the variation of the Lennard-Jones force with the position of particles. If the effect of entropic force is similar to that of the Lennard-Jones force, and other forces are absent, the motion of the cosmological horizon relative to the black hole horizon should have an oscillating process. The entropic force between the two horizons is probably one of the participants in driving the evolution of the universe.

Massive Dirac quasinormal modes in Schwarzschild–de Sitter black holes: Anomalous decay rate and fine structure

Recently, the anomalous decay rate of quasinormal modes has been studied for some geometries under scalar field perturbations, which occurs when the longest-lived modes are the ones with higher angular number, as well as, the existence of a critical scalar field mass, i.e the value of scalar field mass such that the decay rate does not depend appreciably on the angular number, and beyond which the behaviour of the decay rate is inverted. Here, we consider the propagation of fermionic fields in the background of Schwarzschild de Sitter black holes, and we show that the anomalous decay rate behaviour and the fine structure, related to the coupling between the chirality and the mass of the field, can be observed in the fermionic spectrum.

Black hole perturbations of massive and partially massless spin-2 fields in (anti) de Sitter spacetime

We provide a systematic and comprehensive derivation of the linearized dynamics of massive and partially massless spin-2 particles in a Schwarzschild (anti) de Sitter black hole background, in four and higher spacetime dimensions. In particular, we show how to obtain the quadratic actions for the propagating modes and recast the resulting equations of motion in a Schrödinger-like form. In the case of partially massless fields in Schwarzschild de Sitter spacetime, we study the isospectrality between modes of different parity. In particular, we prove isospectrality analytically for modes with multipole number L = 1 in four spacetime dimensions, providing the explicit form of the underlying symmetry. We show that isospectrality between partially massless modes of different parity is broken in higher-dimensional Schwarzschild de Sitter spacetimes.

New rotating AdS/dS black holes in f(R) gravity

It is known that general relativity (GR) theory is not consistent with the latest observations. The modified gravity of GR known as f(R) where R is the Ricci scalar, is considered to be a good candidate for dealing with the anomalies present in classical GR. In this context, we study static rotating uncharged anti-de Sitter and de Sitter (AdS and dS) black holes (BHs) using f(R) theory without assuming any constraints on the Ricci scalar or on f(R). We derive BH solutions depend on the convolution function and deviate from the AdS/dS Schwarzschild BH solution of GR. Although the field equations have no dependence on the cosmological constant, the BHs are characterized by an effective cosmological constant that depends on the convolution function. The asymptotic form of this BH solution depends on the gravitational mass of the system and on extra terms that lead to BHs being different from GR BHs but to correspond to GR BHs under certain conditions. We also investigate how these extra terms are responsible for making the singularities of the invariants milder than those of the GR BHs. We study some physical properties of the BHs from the point of view of thermodynamics and show that there is an outer event horizon in addition to the inner Cauchy horizons. Among other things we show that our BH solutions satisfy the first law of thermodynamics. To check the stability of these BHs we use the geodesic deviations and derive the stability conditions. Finally, using the odd-type mode it is shown that all the derived BHs are stable and have a radial speed equal to one.

Thermodynamics of de Sitter black holes with conformally coupled scalar fields

We investigate the thermodynamic properties of 3+1 dimensional black holes in asymptotically de Sitter spacetimes, conformally coupled to a real scalar field. We use a Euclidean action approach, where boundary value data is specified at a finite radius ‘cavity’ outside the black hole, working in the extended phase space where the cosmological constant is treated as a thermodynamic pressure. We examine the phase structure of these black holes through their free energy. For the MTZ subclass of solutions, we find Hawking-Page-like phase transitions from a black hole spacetime to thermal de Sitter with a scalar field. In the more general case, Hawking-Page-like phase transitions are also present, whose existence depends further on a particular cosmic censorship bound.

Heating up an environment around black holes and inside de Sitter space

We study quantum fields on spacetimes having a bifurcate Killing horizon by allowing the possibility that left- and right- (in-going and out-going) modes have different temperatures. We consider in particular the Rindler for both massless and massive fields, the static de Sitter and Schwarzschild black hole backgrounds for massive fields. We find that in all three cases, when any of the temperatures is different from the canonical one (Unruh, Hawking and Gibbons--Hawking, correspondingly) the correlation functions have extra singularities at the horizon.

Dark energy influence on geodesics of RN–dS space-time

The quintessence influence, as one of the most plausible models of dark energy, on geodesics of Reissner–Nordstrom–de Sitter (RN–dS) black hole is studied. All the possible motions of test particles in the gravitational field are investigated by using the effective potential, and we have done a detailed analysis of the geodesic structure of massless particles and study all kinds of orbits corresponding to the energy levels for this black hole in quintessence field.

Black hole gluing in de Sitter space

We construct dynamical many-black-hole spacetimes with well-controlled asymptotic behavior as solutions of the Einstein vacuum equation with positive cosmological constant. We accomplish this by gluing Schwarzschild–de Sitter or Kerr–de Sitter black hole metrics into neighborhoods of points on the future conformal boundary of de Sitter space, under certain balance conditions on the black hole parameters. We give a self-contained treatment of solving the Einstein equation directly for the metric, given the scattering data we encounter at the future conformal boundary. The main step in the construction is the solution of a linear divergence equation for trace-free symmetric 2-tensors; this is closely related to Friedrich’s analysis of scattering problems for the Einstein equation on asymptotically simple spacetimes.

Semiclassical backreaction on asymptotically anti–de Sitter black holes

We consider a quantum scalar field on the classical background of an asymptotically anti--de Sitter black hole and the backreaction the field's stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semiclassical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page's approximation to the renormalized stress-energy tensor, while for massive fields we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct renormalization freedom required to ensure the semiclassical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in $\ensuremath{\hbar}$) corrections to the metric are obtained. We also compute the corrections to the black hole event horizon, surface gravity, and minimum temperature as well as corrections to the photon sphere and quadratic curvature invariants. We pay particular attention to the temperature profiles of the semiclassical black holes compared with their classical counterparts, pointing out some interesting qualitative features produced by the backreaction. These results ought to provide reasonable approximations to the first-order (one-loop) quantum backreaction on the geometry of asymptotically anti--de Sitter black holes when the exact numerical stress-energy tensor sources the semiclassical equations.

Linear instability of charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet anti de-Sitter black holes * *Peng Liu is Supported by the Natural Science Foundation of China (11847055, 11905083). Chao Niu is Supported by the Natural Science Foundation of China (11805083). C. Y. Zhang is Supported by Natural Science Foundation of China (11947067, 12005077)

We study the linear instability of the charged massless scalar perturbation in regularized 4D charged Einstein-Gauss-Bonnet-AdS black holes by exploring their quasinormal modes. We find that the linear instability is triggered by superradiance. The charged massless scalar perturbation becomes more unstable with increasing Gauss-Bonnet coupling constant or black hole charge. Decreasing the AdS radius, on the other hand, will make the charged massless scalar perturbation more stable. The stable region in parameter space (α, Q, Λ) is given. Moreover, we find that the charged massless scalar perturbation is more unstable for larger scalar charge. The modes of multipoles are more stable than that of the monopole.

Phase transition and entropic force of de Sitter black hole in massive gravity

It is well known that de Sitter(dS) black holes generally have a black hole horizon and a cosmological horizon, both of which have Hawking radiation. But the radiation temperature of the two horizons is generally different, so dS black holes do not meet the requirements of thermal equilibrium stability, which brings certain difficulties to the study of the thermodynamic characteristics of black holes. In this paper, dS black hole is regarded as a thermodynamic system, and the effective thermodynamic quantities of the system are obtained. The influence of various state parameters on the effective thermodynamic quantities in the massive gravity space-time is discussed. The condition of the phase transition of the de Sitter black hole in massive gravity space-time is given. We consider that the total entropy of the dS black hole is the sum of the corresponding entropy of the two horizons plus an extra term from the correlation of the two horizons. By comparing the entropic force of interaction between black hole horizon and the cosmological horizon with Lennard-Jones force between two particles, we find that the change rule of entropic force between the two system is surprisingly the same. The research will help us to explore the real reason of accelerating expansion of the universe.

Origin of the Reissner-Nordström–de Sitter instability

We give strong numerical evidence for the existence of an instability afflicting six-dimensional Reissner-Nordstr\"om de Sitter (RNdS) black holes. This instability is akin of the Konoplya-Zhidenko instability present in RNdS black holes in seven spacetime dimensions and above. Moreover, we perform a detailed analysis of the near-horizon limit of extremal RNdS black holes, and find that unstable gravitational modes effectively behave as a massive scalar field whose mass violates the AdS$_2$ Breitenl\"ohner-Freedman bound (if and only if $d\geq 6$), thus providing a physical argument for the existence of the instability. Finally, we show that the frequency spectrum of perturbations of RNdS has a remarkable intricate structure with several bifurcations/mergers that appears unique to RNdS black holes

Quasinormal modes of Kerr–de Sitter black holes via the Heun function

This note addresses quasinormal mode (QNM) frequencies of four-dimensional asymptotically de Sitter rotating black holes. The main motivation is that Mathematica 12.1 has implemented a new family of special functions: Heun functions. Using the fact that Teukolsky’s equations for Kerr–de Sitter black holes are mapped to Heun’s equations, we are able to compute their QNM frequencies by the Heun function. In this approach, Mathematica normally evaluates these frequencies to arbitrary numerical precision in a few seconds. We further discuss an application to asymptotically flat rotating black holes.

Instability of regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes * *Supported by the National Natural Science Foundation of China (11847055, 11905083, 11805083, 11947067)

We studied the instability of regularized 4D charged Einstein-Gauss-Bonnet de-Sitter black holes under charged scalar perturbations. The unstable modes satisfy the superradiant condition, but not all of the modes satisfying the superradiant condition are unstable. The instability occurs when the cosmological constant is small and the black hole charge is not too large. The Gauss-Bonnet coupling constant further destabilizes black holes when both the black hole charge and the cosmological constant are small and further stabilizes black holes when the black hole charge is large.

Black holes with a fluid of strings

We obtain an exact solution of Einstein’s equations for a charged, static and spherically symmetric body, surrounded by a fluid of strings and with a cosmological constant. This corresponds to the Reissner–Nordström–(de Sitter)–Anti de Sitter black hole surrounded by a fluid of strings. Some aspects concerning the horizons and geodesic motion are discussed. We also obtain the metric corresponding to the Kerr–Newman black hole surrounded by a fluid of strings, by using a method to construct the rotating solution from its counterpart static one. The horizons, ergoregions, and geodesic motion are analyzed. In both cases, the role played by the fluid of strings was pointed out.

Phase transitions and entropy force of charged de Sitter black holes with cloud of string and quintessence

In this paper, we investigate the combined effects of the cloud of strings and quintessence on the thermodynamics of a Reissner–Nordström–de Sitter black hole. Based on the equivalent thermodynamic quantities considering the correlation between the black hole horizon and the cosmological horizon, we extensively discuss the phase transitions of the spacetime. Our analysis proves that similar to the case in AdS spacetime, second-order phase transitions could take place under certain conditions, with the absence of first-order phase transition in the charged de Sitter (dS) black holes with cloud of string and quintessence. The effects of different thermodynamic quantities on the phase transitions are also quantitatively discussed, which provides a new approach to study the thermodynamic qualities of unstable dS spacetime. Focusing on the entropy force generated by the interaction between the black hole horizon and the cosmological horizon, as well as the Lennard–Jones force between two particles, our results demonstrate the strong degeneracy between the entropy force of the two horizons and the ratio of the horizon positions, which follows the surprisingly similar law given the relation between the Lennard–Jones force and the ratio of two particle positions. Therefore, the study of the entropy force between two horizons is not only beneficial to the deep exploration of the three modes of cosmic evolution, but also helpful to understand the correlation between the microstates of particles in black holes and those in ordinary thermodynamic systems.

The solution of a modified Hamilton–Jacobi equation with Lorentz-violating scalar field

A modified Hamilton–Jacobi equation with Lorentz-violating scalar field in the curved spacetime is used to research tunneling radiation from the horizons of Reissner–Nordstr $$\ddot{\mathrm{o}}$$ m de Sitter black hole. We investigate the influence of different etheric-like vector $$u^\alpha $$ on the solution of the modified Hamilton–Jacobi equation by using both the semi-classical approximation and beyond the semi-classical approximation. We find that the solution of the modified Hamilton–Jacobi equation strongly depends on the choices of $$u^\alpha $$ . As $$u^\alpha =\delta ^\alpha _t u^t$$ , the Lorentz-violating scalar field can enhances black holes’ Hawking temperature but reduces its entropy. However, the case will reverses as $$u^\alpha =\delta ^\alpha _r u^r$$ . Our conclusions are applicable to other spherically symmetric charged black holes.

Quasinormal modes and strong cosmic censorship in the regularised 4D Einstein–Gauss–Bonnet gravity

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.

Hawking radiation of Reissner–Nordström–de Sitter black hole with a global monopole derived from modified Hamilton–Jacobi equation

The tunneling characteristics at the cosmological and event horizons of Reissner–Nordström–de Sitter black hole with a global monopole are studied by using the modified Lorentz violation scalar field equation in curved space–time. Firstly, we get the modified Hamilton–Jacobi equation using the semi-classical approximation, then the Hawking radiation and thermodynamical properties of Reissner–Nordström–de Sitter black hole with a global monopole are computed based on the modified Hamilton–Jacobi equation. Our results show that Lorentz violation can lead to lower Hawking temperature and higher entropy of the black hole at the same time. This work improves the understanding of the physical nature of Lorentz violation in curved space–time.