dS Spacetime Research Articles

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.

Thermodynamic quantities and phase transitions of five-dimensional de Sitter hairy spacetime* *Supported by the National Natural Science Foundation of China (12075143)

In this study, we take the mass, electric charge, hair parameter, and cosmological constant of five-dimensional de Sitter hairy spacetime as the state parameters of the thermodynamic system, and when these state parameters satisfy the first law of thermodynamics, the equivalent thermodynamic quantities of spacetime and the Smarr relation of five-dimensional de Sitter hairy spacetime are obtained. Then, we study the thermodynamic characteristics of the spacetime described by these equivalent thermodynamic quantities and find that de Sitter hairy spacetime has a phase transition and critical phenomena similar to those of van de Waals systems or charged AdS black holes. It is shown that the phase transition point of de Sitter hairy spacetime is determined by the ratio of two event horizon positions and the cosmic event horizon position. We discuss the influence of the hair parameter and electric charge on the critical point. We also find that the isochoric heat capacity of the spacetime is not zero, which is consistent with the ordinary thermodynamic system but differs from the isochoric heat capacity of AdS black holes, which is zero. Using the Ehrenfest equations, we prove that the critical phase transition is a second order equilibrium phase transition. Research on the thermodynamic properties of five-dimensional de Sitter hairy spacetime lays a foundation for finding a universal de Sitter spacetime thermodynamic system and studying its thermodynamic properties. Our universe is an asymptotically dS spacetime, and the thermodynamic characteristics of de Sitter hairy spacetime will help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of the accelerated expansion of the universe.

Traversable thin-shell wormhole in the 4D Einstein–Gauss–Bonnet theory

This work investigates the spherically symmetric thin-shell wormhole solutions in four-dimensional Einstein–Gauss–Bonnet theory and explores their stabilities under radial, linear perturbations. These solutions are typically traversable and characterized by a thin-shell throat in accordance with Israel’s junction conditions. In asymptotically flat and AdS spacetimes with a negative Gauss–Bonnet coupling constant, stable neutral wormholes are encountered when the magnitude of the coupling constant becomes significant. The throats of such wormholes are sustained by ordinary matter and possess finite radii. In asymptotically dS spacetimes, no stable neutral wormhole featuring ordinary matter is observed. On the other hand, for positive Gauss–Bonnet coupling constant, stable thin-shell wormhole solutions can be established when the throats are exclusively supported by exotic matter. Moreover, stable charged wormholes comprised of ordinary matter are found universally in the asymptotically flat, AdS, and dS spacetimes. Unlike their neutral counterparts, the throat radii of such charged wormholes can be arbitrarily small. However, as the charge becomes more significant, such solutions only remain stable when supported by exotic matter.

Thermodynamics of phase transition in Reissner–Nordström–de Sitter spacetime

The Reissner-Nordstrm̈-de Sitter (RN-dS) spacetime can be considered as a thermodynamic system. Its thermodynamic properties are discussed that the RN-dS spacetime has phase transitions and critical phenomena similar to that of the Van de Waals system or the charged AdS black hole. The continuous phase transition point of RN-dS spacetime depends on the position ratio of the black hole horizon and the cosmological horizon. We discuss the critical phenomenon of the continuous phase transition of RN-dS spacetime according to Landau theory of continuous phase transition, that the critical exponent of spacetime is same as that of the Van de Waals system or the charged AdS black hole, which have universal physical meaning. We find that the order parameters are similar to those introduced in ferromagnetic systems. Our universe is an asymptotically dS spacetime, thermodynamic characteristics of RN-dS spacetime can help us understand the evolution of spacetime and provide a theoretical basis to explore the physical mechanism of accelerated expansion of the universe.

A type of unifying relation in (A)dS spacetime

Unifying relations of amplitudes are elegant results in flat spacetime, but the research on these in (A)dS case is not very rich. In this paper, we discuss a type of unifying relation in (A)dS by using Berends-Giele currents. By taking the flat limit, we also get a semi-on-shell way to prove the unifying relations in the flat case. We also discuss the applications of our results in cosmology.

Thermodynamics of asymptotically de Sitter black hole in dRGT massive gravity from Rényi entropy

The thermodynamic properties of the de Rham–Gabadadze–Tolley (dRGT) black hole in the asymptotically de Sitter (dS) spacetime are investigated by using Rényi entropy. It has been found that the black hole with asymptotically dS spacetime described by the standard Gibbs–Boltzmann statistics cannot be thermodynamically stable. Moreover, there generically exist two horizons corresponding to two thermodynamic systems with different temperatures, leading to a nonequilibrium state. Therefore, in order to obtain the stable dRGT black hole, we use the alternative Rényi statistics to analyze the thermodynamic properties in both the separated system approach and the effective system approach. Interestingly, we found that it is possible concurrently obtain positive pressure and volume for the dRGT black hole while it is not for the Schwarzschild-de Sitter (Sch-dS) black hole. Furthermore, the bounds on the nonextensive parameter for which the black hole being thermodynamically stable are determined. In addition, the key differences between the systems described by different approaches, e.g., temperature profiles and types of the Hawking–Page phase transition are pointed out.

Black holes in dS3

In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Nariai-type limit. We show explicitly how these solutions arise using braneworld holography, but also compare to a non-holographic, perturbative analysis of backreaction due to conformally coupled scalar fields in conical de Sitter space. We analyze the thermodynamics of this quantum black hole, revealing it behaves similarly to its classical four-dimensional counterpart, where the generalized entropy replaces the classical Bekenstein-Hawking entropy. We compute entropy deficits due to nucleating the three-dimensional black hole and revisit arguments for a possible matrix model description of dS spacetimes. Finally, we comment on the holographic dual description for dS spacetimes as seen from the braneworld perspective.

Instability of de-Sitter black hole with massive scalar field coupled to Gauss–Bonnet invariant and the scalarized black holes

The black hole scalarization in a special Einstein-scalar–Gauss–Bonnet (EsGB) gravity has been widely investigated in recent years. Especially, the spontaneous scalarization of scalar-free black hole in de-Sitter (dS) spacetime possesses interesting features due to the existence of cosmological horizon. In this work, firstly, we focus on the massive scalar field perturbation on Schwarzschild dS (SdS) black hole in a special EsGB theory. By analyzing the fundamental QNM frequency and time evolution of the scalar field perturbation, we figure out the unstable/stable regions in (Lambda ,alpha )-plane as well as in (m,alpha )-plane for various perturbation modes, where Lambda , alpha and m denote the cosmological constant, the GB coupling strength and the mass of scalar field, respectively. Then by solving the static perturbation equation, we analyze the bifurcation point at which the SdS black hole supports spherical scalar clouds, and we find that the bifurcation points match well with alpha _c on the border of unstable/stable region. Finally, after addressing that the scalarised solutions could only emerge from the scalar could with node kge 1. we explicitly construct the scalarized hairy solutions for different scalar masses and compare the profile of scalar field to the corresponding scalar clouds.

Overview of thermodynamical properties for Reissner–Nordström–de Sitter spacetime in induced phase space

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner–Nordström (RN) black hole are not independent with each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN–dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the laws of thermodynamics still hold on. In our work, the thermodynamic properties of the RN–dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN–dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule–Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvatures of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN–dS spacetime, which opens a new window to investigate the dS spacetime with black holes from an observational perspective.

Holographic dark energy from the anti–de Sitter black hole

The anti-de Sitter (AdS) black hole plays an important role in the holographic principle. In this study, the upper bound in energy corresponding to the mass of the Schwarzschild black hole is modified to be that of the AdS black hole. Via the correspondence between the ultraviolet (UV) and infrared (IR) cutoffs, the constant term in the energy density of the holographic dark energy (HDE) can be obtained from the negative cosmological constant from the black hole. Interestingly, the proposed dark energy model could drive the late-time expansion of the Universe without the causality violation. The cosmic evolution is investigated by choosing the Hubble and particle horizons as the IR length scales. It is found that the accelerated expansion at late time can be obtained for both cases. This result may shed light on the connection between the AdS black hole and the de Sitter (dS) spacetime in the context of cosmology.

Hawking–Page phase transition of four-dimensional de-Sitter spacetime with nonlinear source

The interplay between a dS black hole horizon and cosmological horizon in a dS spacetime introduces distinctive thermodynamic behaviors (for example the well-known upper bounds of mass and entropy (Dinsmore et al. in Class. Quant. Grav. 37(5), 2020)). Based on this point, we present the Hawking–Page (HP) phase transition of the four-dimensional dS spacetime with nonlinear charge correction when the effective pressure is fixed, and analyze the effects of different effective pressures and nonlinear charge corrections on HP phase transition. The evolution of this system undergoing the HP phase transition is also investigated. We find that the coexistent curve of HP phase transition is a closed one with two different branches. That indicates there exist the upper bounds of the HP temperature and HP pressure, which is completely distinguished with that in AdS spacetime. With decreasing the distance between two horizons, the dS spacetime at the coexistent curve of HP phase transition is going along with different branches. Furthermore, we also explore the influences of charge and nonlinear charge correction on the coexistent curve.

Continuous phase transition of higher-dimensional de-Sitter spacetime with non-linear source

For the higher-dimensional dS spacetime embedded with black holes with non-linear charges, there are two horizons with different radiation temperatures. By introducing the interplay between two horizons this system can be regarded as an ordinary thermodynamic system in the thermodynamic equilibrium described by the thermodynamic quantities (T_{eff},~P_{eff},~V,~S,~Phi _{eff}). In this work, our focus is on the thermodynamic properties of phase transition for the four-dimensional dS spacetime with different values of the charge correction {bar{phi }}. We find that with the increasing of the non-linear charge correction the two horizons get closer and closer, and the correction entropy is negative which indicates the interaction between the two horizons stronger and stronger. Furthermore, the heat capacity at constant pressure, isobaric expansion coefficient, and the isothermal compression coefficient have the Schottky peak at the critical point. However, the heat capacity as constant volume for the dS spacetime is nonzero. Finally, the dynamical properties of phase transition for this system have investigated based on Gibbs free energy, where exists the different behavior with that for AdS black holes.

Higher-dimensional black holes with multiple equal rotations

We study a limit of the Kerr-(A)dS spacetime in a general dimension where an arbitrary number of its rotational parameters is set equal. The resulting metric after the limit formally splits into two parts - the first part has the form of the Kerr-NUT-(A)dS metric analogous to the metric of the entire spacetime, but only for the directions not subject to the limit, and the second part can be interpreted as the K\"{a}hler metrics. However, this separation is not integrable, thus it does not lead to a product of independent manifolds. We also reconstruct the original number of explicit and hidden symmetries associated with Killing vectors and Killing tensors. Therefore, the resulting spacetime represents a special subcase of the generalized Kerr-NUT-(A)dS metric that retains the full Killing tower of symmetries. In $D=6$, we present evidence of an enhanced symmetry structure after the limit. Namely, we find additional Killing vectors and show that one of the Killing tensors becomes reducible as it can be decomposed into Killing vectors.

Generalized Gravitational Phase Transition in Novel 4D Einstein–Gauss–Bonnet Gravity

AbstractIn this paper, the possible existence of a thermal phase transition from asymptotic anti‐de Sitter (AdS) to de Sitter (dS) geometries in vacuum in the context of the novel fourdimensional Einstein–Gauss–Bonnet (4D EGB) gravity is presented. The phase transition proceeds via a thermalon (the Euclidean section of a bubble thin shell) formation, having a black hole in the dS spacetime and a thermal AdS spacetime in the exterior, without introducing any matter field. From the analysis, it is found that, using regularized novel 4D EGB gravity, the gravitational phase transitions occur for all allowed values of the 4D EGB coupling. In the 4D EGB gravity, the existence of the above phase transition is over a narrow range of the 4D EGB coupling, with particular critical values. In contrast, in five‐dimensional (5D) EGB gravity, a 5D sector needs a wider range of its coupling for the existence of a thermalon, and there also exist critical values for the emergence of the above phase transition.

Noncommutative (A)dS and Minkowski spacetimes from quantum Lorentz subgroups

The complete classification of classical r-matrices generating quantum deformations of the (3 + 1)-dimensional (A)dS and Poincaré groups such that their Lorentz sector is a quantum subgroup is presented. It is found that there exists three classes of such r-matrices, one of them being a novel two-parametric one. The (A)dS and Minkowskian Poisson homogeneous spaces corresponding to these three deformations are explicitly constructed in both local and ambient coordinates. Their quantization is performed, thus giving rise to the associated noncommutative spacetimes, that in the Minkowski case are naturally expressed in terms of quantum null-plane coordinates, and they are always defined by homogeneous quadratic algebras. Finally, non-relativistic and ultra-relativistic limits giving rise to novel Newtonian and Carrollian noncommutative spacetimes are also presented.

Mean field squared and energy–momentum tensor for the hyperbolic vacuum in dS spacetime

We evaluate the Hadamard function and the vacuum expectation values (VEVs) of the field squared and energy–momentum tensor for a massless conformally coupled scalar field in (D+1)-dimensional de Sitter (dS) spacetime foliated by spatial sections of negative constant curvature. It is assumed that the field is prepared in the hyperbolic vacuum state. An integral representation for the difference of the Hadamard functions corresponding to the hyperbolic and Bunch–Davies vacua is provided that is well adapted for the evaluation of the expectation values in the coincidence limit. It is shown that the Bunch–Davies state is interpreted as thermal with respect to the hyperbolic vacuum. An expression for the corresponding density of states is provided. The relations obtained for the difference in the VEVs for the Bunch–Davies and hyperbolic vacua are compared with the corresponding relations for the Fulling–Rindler and Minkowski vacua in flat spacetime. The similarity between those relations is explained by the conformal connection of dS spacetime with hyperbolic foliation and Rindler spacetime. As a limiting case, the VEVs for the conformal vacuum in the Milne universe are discussed.

Hyperbolic metamaterials and massive Klein-Gordon equation in ( 2+1 )-dimensional de Sitter spacetime

The wave equation obeyed by the extraordinary component of the electric field in a hyperbolic metamaterial was shown to be a massless Klein-Gordon field living in a flat spacetime with two timelike and two spacelike dimensions. Such a wave equation, unexpectedly, allows dispersionless propagation albeit having two spatial dimensions. Here we show that the same equation can be naturally interpreted as a particular massive Klein-Gordon equation with the usual one timelike and two spacelike dimensions in a de Sitter (dS) background spacetime. The mass parameter of the scalar field is given in terms of the cosmological constant, Planck constant, and the speed of light as $m=\sqrt{\mathrm{\ensuremath{\Lambda}}}\frac{\ensuremath{\hbar}}{c}$ which corresponds to the point for which the left and right conformal weights of the boundary conformal field theory (CFT) (via the de Sitter/CFT correspondence) are equal. This particular mass corresponds to the gapless mode in the dS spacetime for which the dispersion relation is linear in the wave number.

Frame-Dragging: Meaning, Myths, and Misconceptions

Originally introduced in connection with general relativistic Coriolis forces, the term frame-dragging is associated today with a plethora of effects related to the off-diagonal element of the metric tensor. It is also frequently the subject of misconceptions leading to incorrect predictions, even of nonexistent effects. We show that there are three different levels of frame-dragging corresponding to three distinct gravitomagnetic objects: gravitomagnetic potential 1-form, field, and tidal tensor, whose effects are independent, and sometimes opposing. It is seen that, from the two analogies commonly employed, the analogy with magnetism holds strong where it applies, whereas the fluid-dragging analogy (albeit of some use, qualitatively, in the first level) is, in general, misleading. Common misconceptions (such as viscous-type “body-dragging”) are debunked. Applications considered include rotating cylinders (Lewis–Weyl metrics), Kerr, Kerr–Newman and Kerr–dS spacetimes, black holes surrounded by disks/rings, and binary systems.

Quantum simulation of cosmic inflation

In this paper, we generalize Jordan-Lee-Preskill, an algorithm for simulating flat-space quantum field theories, to 3+1 dimensional inflationary spacetime. The generalized algorithm contains the encoding treatment, the initial state preparation, the inflation process, and the quantum measurement of cosmological observables at late time. The algorithm is helpful for obtaining predictions of cosmic non-Gaussianities, serving as useful benchmark problems for quantum devices, and checking assumptions made about interacting vacuum in the inflationary perturbation theory. Components of our work also include a detailed discussion about the lattice regularization of the cosmic perturbation theory, a detailed discussion about the in-in formalism, a discussion about encoding using the HKLL-type formula that might apply for both dS and AdS spacetimes, a discussion about bounding curvature perturbations, a description of the three-party Trotter simulation algorithm for time-dependent Hamiltonians, a ground state projection algorithm for simulating gapless theories, a discussion about the quantum-extended Church-Turing Thesis, and a discussion about simulating cosmic reheating in quantum devices.