Action, entropy and pair creation rate 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.

Cardy–Verlinde formula and thermodynamics of black holes in de Sitter spaces

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.

Kerr-Newman black holes in a de Sitter (dS) space have the limit of rotating Nariai black holes with the near-horizon geometry of a warped dS3×S1/Z2 when the black hole horizon and the cosmological horizon coincide or approach close to each other. We study the rotation effect on the spontaneous emission of charges in the near-extremal rotating charged Nariai black hole and compare it to those from the near-extremal Nariai black hole in [C.-M. Chen , ] and near-extremal Kerr-Newman black hole in de Sitter space in [C.-M. Chen and S. P. Kim, ]. In strong contrast to the near-extremal Kerr-Newman black hole in dS space, the near-extremal rotating Nariai black hole also has an exponential amplification for the emission of high-energy charges, which becomes catastrophic regardless of angular momentum when two horizons coincide. The radius of rotating Nariai black holes monotonically increases as the angular momentum and charge of black holes increase, which gives a weaker electric field on the horizon than Nariai black holes. Thus, the angular momentum of black holes that drags particles on the horizon decreases the mean number of charges by a factor not by an order. We observe a catastrophic emission of boson condensation for charges with an effective energy equal to the chemical potential in the spacelike outer region of the cosmological horizon. Remarkably, the Schwinger emission of charges in the standard particle model may prevent the rotating Nariai black holes from evolving into spacetimes with a naked singularity when the angular momentum is close to the allowed maximum, which Nariai black holes cannot avoid.

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.

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.

We study the large D effective theory for D dimensional charged (Anti) de Sitter black holes. Then we show that the de Sitter Reissner–Nordstrom black hole becomes unstable against gravitational perturbations at larger charge than a critical charge in a higher dimension. Furthermore, we find that there is a nontrivial zero-mode static perturbation at the critical charge. The existence of static perturbations suggests the appearance of non-spherical symmetric solution branches of static charged de Sitter black holes. This expectation is confirmed by constructing the non-spherical symmetric static solutions of large D effective equations.

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.

The application of nonlinear electrodynamics at high energy scales has led to a variety of interesting phenomena in recent years, particularly within the context of non-singular spacetime geometries. Additionally, it is postulated that gravity near the Planck scale is governed by a minimal cut-off length, which acts as a renormalization scale against ultraviolet pathologies. Within this framework, we combine both concepts by introducing modifications to the electric and matter sectors of a black hole as its size approaches this minimal length. The result is an electrically charged black hole that is free from ultraviolet divergences and recovers the Maxwell limit at classical scales. We further explore the geometric and thermodynamic properties of the resulting solution within a cosmological anti-de Sitter background, revealing a chemical analogy with that of a Van der Waals fluid. Subsequently, we examine the charged black hole in de Sitter space and construct four corresponding gravitational instantons. We then study their cosmological quantum production using the formalism of the pair creation rate within the context of the no-boundary proposal.

Recently, Hawking radiation has been treated, by Robinson and Wilczek (2005 Phys. Rev. Lett. 95 011303), as a compensating flux of the energy–momentum tensor required to cancel a gravitational anomaly at the event horizon (EH) of a Schwarzschild-type black hole. In this paper, motivated by this work, Hawking radiation from the event horizon (EH) and the de Sitter cosmological horizon (CH) of black holes in de Sitter spaces, specifically including the purely de Sitter black hole and the static, spherically symmetric Schwarzschild–de Sitter black hole as well as the rotating Kerr–de Sitter black hole, have been studied by anomalies. The results show that the gauge–current and energy–momentum tensor fluxes, required to restore gauge invariance and general coordinate covariance at the EH and the CH, are precisely equal to those of Hawking radiation from the EH and the CH, respectively. It should be noted that gauge and gravitational anomalies taking place at the CH arise from the fact that the effective field theory is formulated inside the CH to integrate out the classically irrelevant outgoing modes at the CH, which are different from those at the black hole horizon.

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.

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.

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.

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.

Anomalies and de Sitter radiation from the generic black holes in de Sitter spaces