Holes In De Sitter Space Research Articles

Violation of weak cosmic censorship in de Sitter space

Inspired by the recent discovery of a violation of strong cosmic censorship (SCC) for the near-extremal Reissner-Nordström black holes in de Sitter space (RN-dS), we investigate if the weak cosmic censorship conjecture (WCCC) can also be violated in RN-dS with a fixed cosmological constant. Our method is based on the recent formulation of examining WCCC by the constraint of the second law, which in this case requires the sum of areas of the event and cosmic horizons cannot decrease during the infall process of Wald’s gedanken experiment. We find that the WCCC can be violated for the near-extremal RN-dS in some regimes of second-order perturbation of field configurations. Given the charge parameter of RN-dS, we can find the lowest value of the subextremality parameter, beyond which the WCCC holds. Our results imply that there might be possible correlations between the violation of SCC and WCC. Because of a lack of an unambiguous relation between the gravitational mass and matter’s kinematic mass in asymptotically de Sitter space, we cannot compare the corresponding regimes of parameter space for the violations of SCC and WCCC. We also discuss the subtlety in formulating the first- and second-law approaches to examine WCCC. Published by the American Physical Society 2024

Action, entropy and pair creation rate of charged black holes in de Sitter space

We compute and clarify the interpretation of the on-shell Euclidean action for Reissner-Nordström black holes in de Sitter space. We show the on-shell action is minus the sum of the black hole and cosmological horizon entropy for arbitrary mass and charge in any number of dimensions. This unifying expression helps to clear up a confusion about the Euclidean actions of extremal and ultracold black holes in de Sitter, as they can be understood as special cases of the general expression. We then use this result to estimate the probability for the pair creation of black holes with arbitrary mass and charge in an empty de Sitter background, by employing the formalism of constrained instantons. Finally, we suggest that the decay of charged de Sitter black holes is governed by the gradient flow of the entropy function and that, as a consequence, the regime of light, superradiant, rapid charge emission should describe the potential decay of extreme charged Nariai black holes to singular geometries.

Extremal black hole decay in de Sitter space

The decay of extremal charged black holes has been a useful guidance to derive consistency conditions in quantum gravity. In de Sitter space it has been argued that requiring (extremal) charged Nariai black holes to decay without forming a big crunch singularity yields the Festina Lente (FL) bound: particles with mass ms and charge q should satisfy ms2≫MpHq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {m}_s^2\\gg {M}_p Hq $$\\end{document}, where Mp is the Planck mass and H the Hubble parameter. Using a tunneling approach we show that the decay probability of charged black holes in de Sitter space in the s-wave sector is P ∼ exp(∆Sb), where ∆Sb is the change in the black hole entropy. We find that the FL bound corresponds to ∆Sb ≤ – 1 in the Nariai and probe limit. However, taking into account backreaction we identify unsuppressed decay channels, which might be subdominant, that violate this bound but nonetheless do not result in a big crunch for every observer.

On irregular states and Argyres-Douglas theories

Conformal theories of the Argyres-Douglas type are notoriously hard to study given that they are isolated and strongly coupled thus lacking a lagrangian description. In flat space, an exact description is provided by the Seiberg-Witten theory. Turning on a Ω-background makes the geometry “quantum” and tractable only in the weak curvature limit. In this paper we use the AGT correspondence to derive Ω-exact formulae for the partition function, in the nearby of monopole points where the dynamics is described by irregular conformal blocks of the CFT. The results are checked against those obtained by the recursion relations coming from a conformal anomaly in the region where the two approaches overlap. The Nekrasov-Shatashvili limit is also discussed. Finally, we comment on the existence of black holes in De Sitter space whose low energy dynamics is described by an Argyres-Douglas theory.

Quantum corrections to pair production of charged black holes in de Sitter space

We compute Euclidean action of charged de Sitter black holes in four dimensional gravitational Euler-Heisenberg model. It turns out that the action of a general Euclidean dyonically charged black hole is still controlled by the total entropy contributed by the black hole outer horizon and the cosmological horizon. For smooth configurations, the Euclidean action can be interpreted as the black hole production rate in de Sitter space. We show thatthe 4-derivative couplings break the symmetry between the production rate of the purely electric black hole and that of the purely magnetic black hole. Although electromagnetic duality is no longer a symmetry, it induces a transformation on the 4-derivative couplings, mapping the physical quantities of a purely electric black hole to those of a purely magnetic black hole and vice versa. We also observe that under the same transformation, unitarity constraints on the 4-derivative couplings remain invariant.

Charged black holes in de Sitter space: Superradiant amplification of charged scalar waves and resonant hyperradiation

Black holes typically inhabit highly dynamical galactic environments and are frequently permeated by accretion media. The inevitable scattering of scalar, electromagnetic, and gravitational waves off rotating and charged black holes provides a remarkable demonstration of the energy extraction and subsequent amplification of scattered waves under the expense of the compact object's rotational and electromagnetic energy, a phenomenon known as superradiance. Certain circumstances tremendously favor the energy extraction process in such extent that linear superradiant instabilities are triggered. We examine the superradiant amplification of monochromatic charged scalar fields impinging Reissner-Nordstr\"om-de Sitter black holes which are known to exhibit superradiantly unstable quasinormal modes. We find that even though the frequency range of superradiance is reduced when a positive cosmological constant is incorporated, the amplification factors are significantly elevated with respect to those occurring in Reissner-Nordstr\"om spacetime. Intriguingly, we confirm that the long-lived quasinormal resonances that reside in the superradiant regime induce resonant peaks when the wave's frequency matches the real part of the quasinormal mode, regardless of the spacetime's modal stability.

Extended thermodynamics and entropic force of de Sitter space–time with charged Gauss–Bonnet Black Hole

The discovery of new four-dimensional black hole solutions presents a new approach to understand the Gauss–Bonnet gravity in low dimensions. In this paper, we investigate extended thermodynamics and entropic force of de Sitter space–time with charged Gauss–Bonnet black hole. Think of four-dimensional charged Gauss–Bonnet Black Hole in de Sitter space–time as a thermodynamic system, the state parameters of Space–time must satisfy the basic equations of thermodynamics. By using the functional relation between the state parameters in the basic equation, the equivalent temperature and the space–time entropy of the state parameters satisfying the first law of thermodynamics are obtained. The interaction force between the horizon of the black hole and the cosmic horizon is composed of two parts, one of which is proportional to the Gauss–Bonnet factor. The other part is only related to the ratio of the two horizons. The entropic forces between the two event horizons promote the separation of the cosmic horizon from the black hole event horizon, but the entropic forces of the two parts vary with the position ratio of the two event horizons. This paper explores the characteristics of four-dimensional Gauss–Bonnet gravity and seeks for the intrinsic factors of the expansion of the universe by analyzing the variation law of entropy force between two horizons with the position ratio.

The Black Hole Entropy Distance Conjecture and Black Hole Evaporation

AbstractWe extend the recently proposed Black Hole Entropy Distance Conjecture to the case of charged black holes in de Sitter space. By systematically studying distances in the space of black hole geometries with multiple horizons, we find that the distance is generically related to the logarithm of the entropy. From the infinite distance conjecture this predicts the appearance of a massless tower of modes in the limit of infinite entropy. Further, we study the evaporation of these black holes and relate it to the geometric distance. We find that the corresponding distance to the final stage of evaporation is finite. We conclude that evaporation does not lead to the appearance of a light tower of black hole microstates.

Entropy of higher-dimensional charged Gauss–Bonnet black hole in de Sitter space

The fundamental equation of the thermodynamic system gives the relation between the internal energy, entropy and volume of two adjacent equilibrium states. Taking a higher-dimensional charged Gauss–Bonnet black hole in de Sitter space as a thermodynamic system, the state parameters have to meet the fundamental equation of thermodynamics. We introduce the effective thermodynamic quantities to describe the black hole in de Sitter space. Considering that in the lukewarm case the temperature of the black hole horizon is equal to that of the cosmological horizon, we conjecture that the effective temperature has the same value. In this way, we can obtain the entropy formula of spacetime by solving the differential equation. We find that the total entropy contains an extra term besides the sum of the entropies of the two horizons. The corrected term of the entropy is a function of the ratio of the black hole horizon radius to the cosmological horizon radius, and is independent of the charge of the spacetime.

Thermodynamics and phase transition of spherically symmetric black hole in de Sitter space from Rényi statistics

Schwarzschild black holes in a de Sitter background were studied in terms of their thermodynamics based on the R\'enyi statistics. This led to thermodynamically stable black hole configurations for some certain range of black hole radii; namely within this range the corresponding black holes have positive heat capacity. Moreover, for a certain background temperature there can exist at most three configurations of black hole; one among which is thermodynamically stable. These configurations were investigated in terms of their free energies, resulting in the moderate-sized stable black hole configuration being the most preferred configuration. Furthermore, a specific condition on the R\'enyi non-extensive parameter is required if a given hot spacetime were to evolve thermally into the moderate-sized stable black hole.

A Note on the Swampland Distance Conjecture

AbstractWe discuss the Swampland Distance Conjecture in the framework of black hole thermodynamics. In particular, we consider black holes in de Sitter space and we show that the Swampland Distance Conjecture is a consequence of the fact that apparent horizons are always inside cosmic event horizons whenever they exist in the case of fast‐roll inflation. In addition, we show that the Bekenstein and the Hubble entropy bounds for the entropy in a region of spacetime lead similarly to the same conjecture.

Charged fermions and strong cosmic censorship

It was recently shown that the Strong Cosmic Censorship conjecture might be violated for near-extremally-charged black holes in de Sitter space. Here, we extend our study to charged fermionic fields in the exterior of Reissner-Nordström-de Sitter black holes. We identify three families of modes; one related to the photon sphere, a second related to the de Sitter horizon and a third which dominates near extremality. We show that for near-extremally-charged black holes there is a critical fermionic charge below which Strong Cosmic Censorship may potentially be violated. Surprisingly enough, as one approaches extremality even more, violation of Strong Cosmic Censorship may occur even beyond the critical fermionic charge.

Entropy of black holes with multiple horizons

We examine the entropy of black holes in de Sitter space and black holes surrounded by quintessence. These black holes have multiple horizons, including at least the black hole event horizon and a horizon outside it (cosmological horizon for de Sitter black holes and “quintessence horizon” for the black holes surrounded by quintessence). Based on the consideration that the two horizons are not independent each other, we conjecture that the total entropy of these black holes should not be simply the sum of entropies of the two horizons, but should have an extra term coming from the correlations between the two horizons. Different from our previous works, in this paper we consider the cosmological constant as the variable and employ an effective method to derive the explicit form of the entropy. We also try to discuss the thermodynamic stabilities of these black holes according to the entropy and the effective temperature.

Thermodynamic stability of black holes surrounded by quintessence

We study the thermodynamic stabilities of uncharged and charged black holes surrounded by quintessence (BHQ) by means of effective thermodynamic quantities. When the state parameter of quintessence $\omega_q$ is appropriately chosen, the structures of BHQ are something like that of black holes in de Sitter space. Constructing the effective first law of thermodynamics in two different ways, we can derive the effective thermodynamic quantities of BHQ. Especially, these effective thermodynamic quantities also satisfy Smarr-like formulae. It is found that the uncharged BHQ is always thermodynamically unstable due to negative heat capacity, while for the charged BHQ there are phase transitions of the second order. We also show that there is a great deal of difference on the thermodynamic properties and critical behaviors of BHQ between the two ways we employed.

Thermodynamics of horizons: de Sitter black holes and reentrant phase transitions

In this paper we propose a straightforward method for understanding the thermodynamics of black holes in de Sitter space, one that will allow us to study these black holes in a way that is analogous to the anti-de Sitter case. As per usual, we formulate separate thermodynamic first laws for each horizon present in the spacetime, and study their thermodynamics as if they were independent systems characterized by their own temperature. That these systems are not entirely independent and various thermodynamic quantities in them are in fact ‘correlated’ is reflected by the fact that their thermodynamics can be captured by a single Gibbs free energy-like thermodynamic potential. This quantity contains information about possible phase transitions in the system and allows us to uncover a rich phase structure for de Sitter black holes. In particular, we discover reentrant phase transitions for Kerr–dS black holes in six dimensions, a phenomenon recently observed for their six dimensional AdS cousins.

Entropy of Reissner–Nordström–de Sitter black hole

Based on the consideration that the black hole horizon and the cosmological horizon of Reissner-Nordstr\"om black hole in de Sitter space are not independent each other, we conjecture the total entropy of the system should have an extra term contributed from the entanglement between the two horizons, except for the sum of the two horizon entropies. Making use of the globally effective first law and the effective thermodynamic quantities, we derive the total entropy and find that it will diverge as the two horizons tends to coincide.

Quasi-normal modes and the area spectrum of a near extremal de Sitter black hole with conformally coupled scalar field

In this paper, we have studied a black hole in de Sitter space which has a conformally coupled scalar field in the background. This black hole is also known as the MTZ black hole. We have obtained exact values for the quasi-normal mode (QNM) frequencies under massless scalar field perturbations. We have demonstrated that when the black hole is near-extremal, that the wave equation for the massless scalar field simplifies to a Schrödinger type equation with the well-known Pöschl–Teller potential. We have also used sixth-order WKB approximation to compute QNM frequencies to compare with exact values obtained via the Pöschl–Teller method for comparison. As an application, we have obtained the area spectrum using modified Hods approach and show that it is equally spaced.

Charged fermion tunneling from electrically and magnetically charged rotating black hole in de Sitter space

Thermal radiation of electrically charged fermions from a rotating black hole with electric and magnetic charges in de Sitter space is considered. The tunneling probabilities for outgoing and incoming particles are obtained and the Hawking temperature is calculated. The relation for the classical action for the particles in the black hole’s background is also found.

A De Sitter hoedown

Rotating black holes in de Sitter space are known to have interesting limits where the temperatures of the black hole and cosmological horizon are equal. We give a complete description of the thermal phase structure of all allowed rotating black hole configurations. Only one configuration, the rotating Nariai limit, has the black hole and cosmological horizons both in thermal and rotational equilibrium, in that both the temperatures and angular velocities of the two horizons coincide. The thermal evolution of the spacetime is shown to lead to the pure de Sitter spacetime, which is the most entropic configuration. We then provide a comprehensive study of the wave equation for a massless scalar in the rotating Nariai geometry. The absorption cross section at the black hole horizon is computed and a condition is found for when the scattering becomes superradiant. The boundary-to-boundary correlators at finite temperature are computed at future infinity. The quasinormal modes are obtained in explicit form. Finally, we obtain an expression for the expectation value of the number of particles produced at future infinity starting from a vacuum state with no incoming particles at past infinity. Some of our results are used to provide further evidence for a recent holographic proposal between the rotating Nariai geometry and a two-dimensional conformal field theory.

Extended black hole cosmologies in de Sitter space

We generalize the superposition principle for time-symmetric initial data of black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue problem for a conformal scale ϕ applied to a metric gij with constant three-curvature Rg. Here, Rg = 0, 2 in the Brill–Lindquist and, respectively, the Misner construction of multihole solutions for Λ = 0. For de Sitter and anti-de Sitter cosmologies, we express the result for Rg = 0 in incomplete elliptic functions. The topology of a black hole in de Sitter space can be extended into an infinite tower of universes, across the turning points at the black hole and cosmological event horizons. Superposition introduces binary black holes for small separations and binary universes for separations largely relative to the cosmological event horizon. The evolution of the metric can be described by a hyperbolic system of equations with a curvature-driven lapse function, of alternating sign at successive cosmologies. The computational problem of interacting black hole universes is conceivably of interest to early cosmology when Λ was large and black holes were of mass , here facilitated by a metric which is singularity-free and smooth everywhere on real coordinate space.