dS Spacetime Research Articles

Carroll black holes in (A)dS spacetimes and their higher-derivative modifications

Carroll black holes in (A)dS spacetimes and their higher-derivative modifications

Non-linear charged dS spacetime and its thermodynamics and Schottky Anomaly

Abstract In this paper, firstly, the conditions and existence region for the coexistence of the black hole and cosmological horizons in Non-linear charged dS (NLC-dS) spacetime are discussed, subsequently, the thermodynamic quantities for which the boundary conditions are satisfied in spacetime in the coexistence region of the two horizons are discussed, and the effective thermodynamic quantities in the NLC-dS spacetime in the coexistence region with two horizons are presented. Based on these, the heat capacity in the coexistence region with two horizons is addressed, the behavior of the heat capacity in the NLC-dS spacetime in the aforementioned region is found to exhibit the characteristics of Schottky specific heat. In order to investigate the intrinsic reason of the heat capacity in spacetime, regarding the two horizons in the NLC-dS spacetime as two distinct energy levels, consequently, the microscopic particles at different horizons exhibit disparate energies. Using the heat capacity relationship between the two-energy level in an ordinary thermodynamic system, the heat capacity in dS spacetime is discussed, it is observed that the behavior of the heat capacity is analogous to that of the two-energy levels in an ordinary thermodynamic system. The number of microscopic particles in the two-level system is approximated by comparing the maximum value of the heat capacity of the system with the maximum value obtained by treating the two horizons in the NLC-dS spacetime as a two-energy-level system of two distinct energies. This conclusion reflects the quantum properties of the coexistence region with two horizons in the NLC-dS spacetime. It provides a new avenue for further study of the thermodynamic properties of black holes and the quantum properties of de Sitter spacetime.

Flat-space limit of holographic pseudoentropy in (A)dS spacetimes

The real part of pseudoentropy in conformal field theories is holographically calculated by the area of some extremal spacelike surfaces in the dual de Sitter (dS) and anti–de Sitter (AdS) spacetimes. We show that the flat-space limit of these curves in three-dimensional (A)dS spacetimes is well defined. We find that, if the length of the curves is calculated from the radial coordinate where the retarded time is extremum, then after taking the flat-space limit, the entanglement entropy of the dual theory of three-dimensional flat spacetime is obtained. For dS spacetime, the radial coordinate corresponding to the extremum of retarded time is located inside the cosmological horizon. Our results suggest that, on the field theory side, the entanglement entropy in the dual theory of flat spacetimes should be obtained from the ultrarelativistic limit of pseudoentropy in the dual conformal field theory to (A)dS spacetimes. Published by the American Physical Society 2024

Nonexistence of Majorana fermions in Kerr-Newman type spacetimes with nontrivial charge* *Supported by the National Natural Science Foundation of China (12326602)

We show that the Dirac equation is separated into four differential equations for time-periodic Majorana fermions in Kerr-Newman and Kerr-Newman-(A)dS spacetimes. Although they cannot be transformed into radial and angular equations, the four differential equations yield two algebraic identities. When the electric or magnetic charge is nonzero, they conclude that there is no differentiable time-periodic Majorana fermions outside the event horizon in Kerr-Newman and Kerr-Newman-AdS spacetimes, or between the event horizon and the cosmological horizon in Kerr-Newman-dS spacetime.

Scale and conformal invariance on (A)dS spacetimes

We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general two-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension D>4, these conformal theories can be diagonalized into standard massive fields in which unbroken conformal symmetry nontrivially mixes components of different spins. In D=4, the tensor case becomes a conformal theory mixing a partially massless spin-2 field with a massless spin-1 field. For massless linearized gravity in D=4, we confirm through direct calculation that correlation functions of gauge-invariant operators take the conformally invariant form, despite the absence of standard conformal symmetry at the level of the action. Published by the American Physical Society 2024

Physically viable and stable charged perfect fluid solution within [formula omitted] gravity

In this work, we investigate the physical behavior and stability of compact stars in F(Q) gravity. We employ the Buchdahl metric to examine the dynamics of a relativistic, newly charged, isotropic fluid model. The interplay between gravity and electromagnetism is included in the analysis of the system by taking into account the charged state of the fluid, providing insights into how charged fluids behave in gravitational theories. The exterior solution under Schwarzschild–de Sitter (dS) spacetime is linked to the interior solution at the boundary to identify the constants. It is important to note that the Buchdahl ansatz provides a mathematically viable solution for a given transformation in the context of electric charge when pressure and density are maximum in the center and monotonically fall towards the boundary. We have taken into account the compact star Her X-1 with M=(0.85±0.15)M⊙; Radius =13.26−1.08+1.08 km for graphical analysis. In the context of F(Q), the physical acceptability of the model has been examined by looking at the required physical attributes, such as energy conditions, causality, hydrostatic equilibrium, pressure–density ratio, etc. that are satisfied throughout the stellar configuration. It is concluded that the present approach allows a suitable modeling of astrophysical compact objects in F(Q) gravity.

Higher-spin self-dual General Relativity: 6d and 4d pictures, covariant vs. lightcone

We study the higher-spin extension of self-dual General Relativity (GR) with cosmological constant, proposed by Krasnov, Skvortsov and Tran. We show that this theory is actually a gauge-fixing of a 6d diffeomorphism-invariant Abelian theory, living on (4d spacetime)×(2d spinor space) modulo a finite group. On the other hand, we point out that the theory respects the 4d geometry of a self-dual GR solution, with no backreaction from the higher-spin fields. We also present a lightcone ansatz that reduces the covariant fields to one scalar field for each helicity. The field equations governing these scalars have only cubic vertices. We compare our lightcone ansatz to Metsaev’s lightcone formalism. We conclude with a new perspective on the lightcone formalism in (A)dS spacetime: not merely a complication of its Minkowski-space cousin, it has a built-in Lorentz covariance, and is closely related to Vasiliev’s concept of unfolding.

Holographic vacuum energy regularization and corrected entropy of de Sitter space

Abstract We propose that the spectrum of the surface area of the apparent horizon (AH) of de Sitter (dS) spacetime leads to corrected temperature and entropy of the dS spacetime, offering new insights into its thermodynamic properties. This is done by employing the spectrum of the AH radius, acquired from the Wheeler--DeWitt (WDW) equation, together with the Stefan--Boltzmann law, the time-energy uncertainty relation, and the unified first law of thermodynamics.

Spinor-helicity representations of particles of any mass in dS4 and AdS4 spacetimes

The spinor-helicity representations of massive and (partially) massless particles in four-dimensional (anti–)de Sitter (A)dS spacetime are studied within the framework of the dual pair correspondence. We show that the dual groups (also known as “little groups”) of the anti–de Sitter and de Sitter groups are, respectively, O(2N) and O*(2N). For N=1, the generator of the dual algebra so(2)≅so*(2)≅u(1) corresponds to the helicity operator, and the spinor-helicity representation describes massless particles in (A)dS4. For N=2, the dual algebra is composed of two ideals, s and mΛ. The former ideal s≅so(3) fixes the spin of the particle, while the mass is determined by the latter ideal mΛ, which is isomorphic to so(2,1), iso(2), or so(3) depending on the cosmological constant being positive, zero, or negative. In the case of a positive cosmological constant, namely dS4, the spinor-helicity representation contains all massive particles corresponding to the principal series representations and the partially massless particles corresponding to the discrete series representations leaving out only the light massive particles corresponding to the complementary series representations. The zero and negative cosmological constant cases, which had been addressed in earlier references, are also discussed briefly. Finally, we consider the multilinear form of helicity spinors invariant under (A)dS group, which can serve as the (A)dS counterpart of the scattering amplitude, and discuss technical differences and difficulties of the (A)dS cases compared to the flat spacetime case. Published by the American Physical Society 2024

Quantum transitions, detailed balance, black holes, and nothingness

We consider vacuum transitions by bubble nucleation among 4D vacua with different values and signs of the cosmological constant Λ, including both up and down tunnelings. Following the Hamiltonian formalism, we explicitly compute the transition probabilities for all possible combinations of initial and final values of Λ and find that up tunneling is allowed starting not only from dS spacetime but also from AdS and Minkowski spacetimes. We trace the difference with the Euclidean approach, where these transitions are found to be forbidden, to the difference of treating the latter spacetimes as pure (vacuum) states rather than mixed states with correspondingly vanishing or infinite entropy. We point out that these transitions are best understood as limits of the corresponding transitions with black holes in the zero mass limit M→0. We find that detailed balance is satisfied provided we use the Hartle-Hawking sign of the wave function for nucleating spacetimes. In the formal limit Λ→−∞, the transition rates for anti–de Sitter (AdS) to dS agree with both the Hartle-Hawking and Vilenkin amplitudes for the creation of dS from nothing. This is consistent with a proposal of Brown and Dahlen to define “nothing” as AdS in this limit. For M≠0, the detailed balance is satisfied only in a range of mass values. We compute the bubble trajectory after nucleation and find that, contrary to the M=0 case, the trajectory does not correspond to the open universe slicing of dS. We briefly discuss the relevance of our results to the string landscape. Published by the American Physical Society 2024

Rotating detectors in dS and AdS spacetimes

Rotating detectors in dS and AdS spacetimes

BCS in the sky: signatures of inflationary fermion condensation

We consider a Bardeen-Cooper-Schrieffer (BCS)-like model in the inflationary background. We show that with an axial chemical potential, the attractive quartic fermion self-interaction can lead to a BCS-like condensation. In the rigid-de Sitter (dS) limit of inflation where backreaction from the inflaton and graviton is neglected, we perform the first computation of the non-perturbative effective potential that includes the full spacetime curvature effects in the presence of the chemical potential, subject to the mean-field approximation whose validity has been checked via the Ginzburg criterion. The corresponding BCS phase transition is always first-order, when the varying Hubble is interpreted as an effective Gibbons-Hawking temperature of dS spacetime. In the condensed phase, the theory can be understood from UV and IR sides as fermionic and bosonic, respectively. This leads to distinctive signatures in the primordial non-Gaussianity of curvature perturbations. Namely, the oscillatory cosmological collider signal is smoothly turned off at a finite momentum ratio, since different momentum ratios effectively probe different energy scales. In addition, such BCS phase transitions can also source stochastic gravitational waves, which are feasible for future experiments.

Extension of the Schwarzschild black hole solution in f(R) gravitational theory and its physical properties

The successes of f(R) gravitational theory as a logical extension of Einstein’s theory of general relativity (GR) encourage us to delve deep into this theory and continue our study to attempt to derive an extension of the Schwarzschild black hole (BH) solution. In this study, in order to solve the output nonlinear differential equation, we closed the form of the system by assuming the derivative of f(R) with respect to the scalar curvature R to have the form F(r)=df(R(r))dR(r)=1-αr4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(r)=\\frac{\ extrm{d}f(R(r))}{\ extrm{d}R(r)}=1- \\frac{\\alpha }{r^4}$$\\end{document}, where α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} is a dimensional constant. Our study shows that when α→0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \\rightarrow 0$$\\end{document}, we obtain the Schwarzschild BH solution of GR assuming some constraints on the constant of integration, and if these constraints are bounded, we obtain the anti-de Sitter (AdS)/de Sitter (dS) spacetime. For the general case, i.e., when α≠0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha \ e 0$$\\end{document}, we obtain a BH solution that tends asymptotically to AdS/dS spacetime. Moreover, we derive the timelike and null particle geodesics of the BH solution studied in this article. The equation of motion and effective potential of test particles are calculated to study the stability of radial orbits (trajectories). The energy and angular momentum are calculated to study the circular motion and stability of circular orbits. We also derive the stability condition using the geodesic deviation. Moreover, we discuss the physics of the output BH solutions through calculation of the thermodynamic quantities including entropy, the Hawking temperature, and Gibbs free energy. Finally, we check the validity of the first law of thermodynamics applied to the BH of this study. Although we can derive a Schwarzschild black hole solution in the lower order of f(R), specifically when f(R)=R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)=R$$\\end{document}, where the gravitational mass is generated from the source of gravity, we demonstrate that in the higher orders of f(R), when f(R)≠R\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R)\ e R$$\\end{document}, the source of gravity is attributed primarily to higher-order corrections, and the source of gravity that was originally derived from the Schwarzschild black hole has ceased to be dominant.

Semiclassical geometry in double-scaled SYK

We argue that at finite energies, double-scaled SYK has a semiclassical approximation controlled by a coupling λ in which all observables are governed by a non-trivial saddle point. The Liouville description of double-scaled SYK suggests that the correlation functions define a geometry in a two-dimensional bulk, with the 2-point function describing the metric. For small coupling, the fluctuations are highly suppressed, and the bulk describes a rigid (A)dS spacetime. As the coupling increases, the fluctuations become stronger. We study the correction to the curvature of the bulk geometry induced by these fluctuations. We find that as we go deeper into the bulk the curvature increases and that the theory eventually becomes strongly coupled. In general, the curvature is related to energy fluctuations in light operators. We also compute the entanglement entropy of partially entangled thermal states in the semiclassical limit.

A half de Sitter holography

A long-standing and intriguing question is: does the holographic principle apply to cosmologies like de Sitter spacetime? In this work, we consider a half dS spacetime wherein a timelike boundary encloses the bulk spacetime, presenting a version of de Sitter holography. By analyzing the holographic entanglement entropy in this space and comparing it with that in AdS/CFT, we argue that gravity on a half dSd+1 is dual to a highly non-local field theory residing on dSd boundary. This non-locality induces a breach in the subadditivity of holographic entanglement entropy. Remarkably, this observation can be linked to another argument that time slices in global de Sitter space overestimate the degrees of freedom by redundantly counting the same Hilbert space multiple times.

Topological classes of black holes in de-Sitter spacetime

In this paper, we investigate the topological number of de-Sitter black hole solutions with different charges (q) and rotational (a) parameters. By using generalized free energy and Duan’s ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document}-mapping topological current theory, we find that the topological numbers of black holes can still be classified into three types. In addition, we interestingly found the topological classes for de-Sitter (dS) spacetime with distinct horizons, i.e., black hole event horizon and cosmological horizon, will be different. Moreover, we also investigate topological classifications of dS black hole solutions in higher dimensions with or without the Gauss-Bonnet term.

Double Kerr-Schild spacetimes and the Newman-Penrose map

The Newman-Penrose map, which is closely related to the classical double copy, associates certain exact solutions of Einstein’s equations with self-dual solutions of the vacuum Maxwell equations. Here we initiate an extension of the Newman-Penrose map to a broader class of spacetimes. As an example, we apply principles from the Newman-Penrose map to associate a self-dual gauge field to the Kerr-Taub-NUT-(A)dS spacetime and we show that the result agrees with previously studied examples of classical double copies. The corresponding field strength exhibits a discrete electric-magnetic duality that is distinct from its (Hodge star) self-dual property.

Charged spherically symmetric black holes in scalar-tensor Gauss–Bonnet gravity

We derive a novel class of four-dimensional black hole (BH) solutions in Gauss–Bonnet (GB) gravity coupled with a scalar field in presence of Maxwell electrodynamics. In order to derive such solutions, we assume the ansatz for metric potentials. Due to the choice of the ansatz of the metric, the Reissner Nordström gauge potential cannot be recovered because of the presence of higher-order terms which are not allowed to be vanishing. Moreover, the scalar field is not allowed to vanish. If it vanishes, a function of the solution results undefined. Furthermore, it is possible to show that the electric field is of higher-order in the monopole expansion: this fact explicitly comes from the contribution of the scalar field. Therefore, we can conclude that the GB scalar field acts as non-linear electrodynamics creating monopoles, quadrupoles, etc in the metric potentials. We compute the invariants associated with the BHs and show that, when compared to Schwarzschild or Reissner–Nordström space-times, they have a soft singularity. Also, it is possible to demonstrate that these BHs give rise to three horizons in AdS space-time and two horizons in dS space-time. Finally, thermodynamic quantities can be derived and we show that the solution can be stable or unstable depending on a critical value of the temperature.

Particle dynamics around the Einstein–Maxwell–Yang–Mills black hole

The presence of matter in general relativity can cause spacetime to curve. This paper investigates the spacetime properties of the Einstein–Maxwell–Yang–Mills (EMYM) black hole by discussing the geodesic motion of neutral and charged particles. By studying the Lagrangian of these particles, equations of motion and effective potential are obtained in the asymptotic flat and (A)dS spacetimes. Moreover, for the motion of a neutral particle, it is found that there exist stable elliptic/hyperbolic orbits and unstable orbits with different energies by discussing the effective potential and the phase-plane analysis. However, for the motion of a charged particle, there exists an equilibrium point that separates these orbits. In addition, the effects of the system parameters on the potential are analyzed, including the masses of the black hole and charged particles, charges, the cosmological constant, and the strength of the external magnetic field.

Continuous phase transition of the de Sitter spacetime with charged black holes and cloud of strings and quintessence* *Supported by the Natural Science Foundation of China (11705106, 12075143), the Scientific Innovation Foundation of the Higher Education Institutions of Shanxi Province (2020L0471, 2020L0472), the Science Technology Plan Project of Datong City, China (2020153), the Science Foundation of Shanxi Datong University (2022Q1,

Recently, some meaningful results have been obtained by studying the phase transition, critical exponents, and other thermodynamical properties of different black holes. Especially for the Anti-de Sitter (AdS) black holes, their thermodynamical properties nearby the critical point have attracted considerable attention. However, there exists little work on the thermodynamic properties of the de Sitter (dS) spacetime with black holes. In this paper, based on the effective thermodynamical quantities and the method of the Maxwell's equal-area law, we explore the phase equilibrium for the de Sitter spacetime with the charged black holes and the cloud of string and quintessence (i.e., C-dSSQ spacetime). The boundaries of the two-phase coexistence region in both and diagrams are obtained. The coexistent curve and the latent heat of phase transition for this system are also investigated. Furthermore, we analyze the effect of parameters (the state parameter ω and the ratio of two horizon radii /) on the two-phase coexistence region boundary. The results indicate that the phase transition in C-dSSQ spacetime is analogous to that in a van der Waals fluid (vdw) system, which is determined by the electrical potential at the horizon. These results are helpful for understanding the basic properties of black holes and are also of great value for the establishment of quantum gravity.