dS Spacetime Research Articles

Flat Ads Space Evolved into ds Space

This article proposes an educated guess. Since the extreme value of the doubt way of thinking represents the minimum (the breakdown or decline of something into random disorder) of an open (related to tiny, weird movements of atoms) system, we saw in the previous article that the extreme value of the doubt way of thinking can be smaller, which points to that (the breakdown or decline of something into random disorder) reduction acts on the (related to tiny, weird movements of atoms) system. It will happen in a sudden and unplanned way. We assume that the macro system and the micro system are closed systems, the system (the breakdown) increases to 0, the macro open system increases in (the breakdown or decline of something into random disorder), and the micro system decreases in (the breakdown or decline of something into random disorder). We know that Ads space can make up/be equal to Ads/CFT explanation (of why something works or happens the way it does), while ds space has serious (problems, delays, etc.) (experiments prove that the universe is ds space-time). Assuming that there is an unplanned reduction process in the tiny system, the Ads space can change into a ds space.

Charge algebra in Al(A)dSn spacetimes

The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

Entanglement entropy of causal set de Sitter horizons

de Sitter (dS) cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set dS horizons, using Sorkin’s spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the causal set SSEE for the Rindler-like wedge of a symmetric slab of dS spacetime in d = 2, 4 spacetime dimensions using the Sorkin–Johnston vacuum state. We find that the SSEE obeys an area law when the spectrum of the Pauli–Jordan operator is appropriately truncated in both the dS slab as well as its restriction to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume law. This is in agreement with Sorkin and Yazdi’s calculations for the causal set SSEE for nested causal diamonds in , where they showed that an area law is obtained only after truncating the Pauli–Jordan spectrum. In this work we explore different truncation schemes with the criterion that the SSEE so obtained obeys an area law.

Verifying the universe is another way to ds space-time

In this paper, it is explained that the role of the cosmological constant in the De Sitter space is similar to that of the preset boundary conditions in the superradiation phenomenon. In the previous literature, superradiance at a given boundary condition can cause the uncertainty principle to be less extreme, and so the uncertainty principle to be less extreme without the given boundary condition, might be one way to prove that the universe is ds spacetime.

Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr\u2013Newman\u2013de Sitter and Kerr\u2013Newman black hole geometries

We investigate the redshift and blueshift of light emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specifically we compute the redshift and blueshift of photons that are emitted by geodesic massive particles and travel along null geodesics towards a distant observer-located at a finite distance from the KN(a)dS black hole. For this purpose we use the killing-vector formalism and the associated first integrals-constants of motion. We consider in detail stable timelike equatorial circular orbits of stars and express their corresponding redshift/blueshift in terms of the metric physical black hole parameters (angular momentum per unit mass, mass, electric charge and the cosmological constant) and the orbital radii of both the emitter star and the distant observer. These radii are linked through the constants of motion along the null geodesics followed by the photons since their emission until their detection and as a result we get closed form analytic expressions for the orbital radius of the observer in terms of the emitter radius, and the black hole parameters. In addition, we compute exact analytic expressions for the frame dragging of timelike spherical orbits in the KN(a)dS spacetime in terms of multivariable generalised hypergeometric functions of Lauricella and Appell. We apply our exact solutions of timelike non-spherical polar KN geodesics for the computation of frame-dragging, pericentre-shift, orbital period for the orbits of S2 and S14 stars within the 1^{prime prime } of SgrA*. We solve the conditions for timelike spherical orbits in KN(a)dS and KN spacetimes. We present new, elegant compact forms for the parameters of these orbits. Last but not least we derive a very elegant and novel exact formula for the periapsis advance for a test particle in a non-spherical polar orbit in KNdS black hole spacetime in terms of Jacobi’s elliptic function sn and Lauricella’s hypergeometric function F_D.

Static spacetimes haunted by a phantom scalar field. III. Asymptotically (A)dS solutions

The static and spherically symmetric solutions in $n(\ge 4)$-dimensional Einstein-phantom-scalar system fall into three family: (i) the Fisher solution, (ii) the Ellis-Gibbons solution, and (iii) the Ellis-Bronnikov solution. We exploit these solutions as seed to generate a bunch of corresponding asymptotically (A)dS spacetimes, at the price of introducing the potential of the scalar field. Despite that the potentials are different for each solution, each potential is expressed in terms of the superpotential as in supergravity. We discuss the global structure of these solutions in detail and spell out the domain of parameters under which each solution represents a black hole/wormhole. The Ellis-Bronnikov class of solutions presents novel examples of spherical traversable wormholes that interpolate two different (A)dS critical points of the (super)potential.

Stability and quasinormal modes of black holes in conformal Weyl gravity

In this paper, we first investigate the thermal stability of black holes in conformal Weyl gravity with a comparison with the Schwarzschild black holes. Then, we consider a minimally coupled massive scalar perturbation and calculate the quasinormal modes in asymptotically dS spacetime by employing the sixth order WKB approximation and asymptotic iteration method. The deviations from those of the Schwarzschild-dS solutions are obtained and the possibility of the presence of quasi-resonance modes for Weyl black hole solutions is investigated. Finally, we consider a massless scalar perturbation in the background of asymptotically AdS solutions and calculate the quasinormal modes by using the pseudospectral method. The effects of the free parameter of the theory on the quasinormal modes are studied and deviations from those of the Schwarzschild-AdS black holes are investigated. The imaginary part of quasinormal frequencies in AdS spacetime is the time scale of a thermal state (in the conformal field theory) to approach thermal equilibrium.

Uniqueness of non-trivial spherically symmetric black hole solution in special classes of F(R) gravitational theory

We show, in detail, that the only non-trivial black hole (BH) solutions for a neutral as well as a charged spherically symmetric space-times, using the class F(R)=R±F1(R), must-have metric potentials in the form h(r)=12−2Mr and h(r)=12−2Mr+q2r2. These BHs have a non-trivial form of Ricci scalar, i.e., R=1r2 and the form of F1(R)=∓R3M. We repeat the same procedure for (Anti-)de Sitter, (A)dS, space-time and got the metric potentials of neutral as well as charged in the form h(r)=12−2Mr−2Λr23 and h(r)=12−2Mr+q2r2−2Λr23, respectively. The Ricci scalar of the (A)dS space-times has the form R=1+8r2Λr2 and the form of F1(R)=∓2R−8Λ3M. We calculate the thermodynamical quantities, Hawking temperature, entropy, quasi-local energy, and Gibbs-free energy for all the derived BHs, that behaves asymptotically as flat and (A)dS, and show that they give acceptable physical thermodynamical quantities consistent with the literature. Finally, we prove the validity of the first law of thermodynamics for those BHs.

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.

Topological charge and black hole photon spheres

Black hole photon spheres or light rings are closely linked to astronomical phenomena, such as the gravitational waves and the shadow in spherically symmetric or axi-symmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett. 124, 181101 (2020)], a topological argument was applied for the four dimensional stationary, axi-symmetric, asymptotically flat black hole, and the result indicates that at least, there exists one standard light ring outside the black hole horizon for each rotation sense. Inspired by it, in this paper, we would like to consider a similar issue for a nonrotating, static, spherically symmetric black hole not only with asymptotically flat behavior, but also with AdS and dS behaviors. Following Duan's topological current $\phi$-mapping theory, the topological current and charge for the photon spheres are introduced. The topological current is nonzero only at the zero point of the vector field determining the location of the photon sphere. So each photon sphere can be assigned a topological charge. Considering the full exterior region, we find the total topological charge always equals -1. This result confirms that there exists at least one standard photon sphere outside of the black hole not only in asymptotically flat spacetime, but also in asymptotically AdS and dS spacetime. Then we apply the study to the dyonic black holes. We observe that even when more photon spheres are included, the total topological charge stays unchanged. Moreover, for a naked singularity, it has a vanishing topological charge, indicating that the black hole and naked singularity are in different topological classes. It is expected that this novel topological argument could provide an insightful idea on the study of the black hole photon spheres or light rings, and further cast new light on the black hole astronomical phenomena.

Rotating and charged Taub-NUT-(A)dS spacetimes on a 3-brane

We construct novel solutions to the effective Einstein equation with four dimensional cosmological constant on a 3-brane in Randall-Sundrum II scenario. The charged solution is obtained by assuming the existence of localized Maxwell fields on the 3-brane. Timelike and null circular geodesics in the neutral rotating braneworld spacetime with NUT parameter are discussed, and we find that such geodesics cannot occur on the equatorial plane. On non-equatorial planes, timelike circular geodesics can occur for the negative tidal charge, but we cannot find numerical results to support the existence of non-equatorial null circular geodesics.

Null geodesics, quasinormal modes, and thermodynamic phase transition for charged black holes in asymptotically flat and dS spacetimes * * Supported by the National Natural Science Foundation of China (11675064, 11875151, 11522541), the Fundamental Research Funds for the Central Universities (lzujbky-2019-it21). S.-W. Wei was also Supported by the Chinese Scholarship Council (CSC) Scholarship (201806185016) to visit the University of Waterloo

A numerical study has indicated that there exists a relation between the quasinormal modes and the Davies point for a black hole. In this paper, we analytically study this relation for charged Reissner-Nordström black holes in asymptotically flat and de Sitter (dS) spacetimes in the eikonal limit, under which the quasinormal modes can be obtained from the null geodesics using the angular velocity and the Lyapunov exponent of the photon sphere. Both in asymptotically flat and dS spacetimes, we observe spiral-like shapes in the complex quasinormal mode plane. However, the starting point of the shapes does not coincide with the Davies point. Nevertheless, we find a new relation in which the Davies point exactly meets the maximum temperature T in the T- and T- planes. In a higher-dimensional asymptotically flat spacetime, although there is no spiral-like shape, such a relation still holds. Therefore, we provide a new relation between black hole thermodynamics and dynamics in the eikonal limit. Applying this relation, we can test the thermodynamic property of a black hole using the quasinormal modes.

Low-dimensional de Sitter quantum gravity

We study aspects of Jackiw-Teitelboim (JT) quantum gravity in two-dimensional nearly de Sitter (dS) spacetime, as well as pure de Sitter quantum gravity in three dimensions. These are each theories of boundary modes, which include a reparameterization field on each connected component of the boundary as well as topological degrees of freedom. In two dimensions, the boundary theory is closely related to the Schwarzian path integral, and in three dimensions to the quantization of coadjoint orbits of the Virasoro group. Using these boundary theories we compute loop corrections to the wavefunction of the universe, and investigate gravitational contributions to scattering.Along the way, we show that JT gravity in dS2 is an analytic continuation of JT gravity in Euclidean AdS2, and that pure gravity in dS3 is a continuation of pure gravity in Euclidean AdS3. We define a genus expansion for de Sitter JT gravity by summing over higher genus generalizations of surfaces used in the Hartle-Hawking construction. Assuming a conjecture regarding the volumes of moduli spaces of such surfaces, we find that the de Sitter genus expansion is the continuation of the recently discovered AdS genus expansion. Then both may be understood as coming from the genus expansion of the same double-scaled matrix model, which would provide a non-perturbative completion of de Sitter JT gravity.

Constraint on the radius of five-dimensional dS spacetime with GW170817 and GRB 170817A

The recent detections of the gravitational wave (GW) event GW170817 and its electromagnetic counterpart GRB 170817A produced by a binary neutron star (NS) merger is a new milestone of multimessenger astronomy. The time interval between these two signals has attracted widespread attention from physicists. In the braneworld scenario, GWs could propagate through the bulk while electromagnetic waves (EMWs) are bounded on the brane, i.e., our Universe. Therefore, the trajectories of GWs and EMWs may follow different pathes. If GWs and EMWs are originated simultaneously from the same source on the brane, they are expected to arrive at the observer successively. Consequently, the time delay between GW170817 and GRB 170817A may carry the information of the extra dimension. In this paper, we try to investigate the phenomenon in the context of a five-dimensional dS ($\text{dS}_5$) spacetime. We first study two special Universe models, i.e., de Sitter and Einstein-de Sitter models, and calculate the gravitation horizon radius in each case. For the real Universe, we then consider the $\Lambda$CDM model. Our results show that for the de Sitter model of the Universe, the $\text{dS}_5$ radius could not contribute to the time delay. With the data of the observation, we constrain the $\text{dS}_5$ radius to $\ell\gtrsim7.5\times10^{2}\,\text{Tpc}$ for the Einstein-de Sitter model and $\ell\gtrsim2.4\times10^{3}\,\text{Tpc}$ for the $\Lambda$CDM model. After considering the uncertainty in the source redshift and the time-lags given by different astrophysical processes of the binary NS merger, we find that our constraints are not sensitive to the redshift in the range of (0.005, 0.01) and the time-lag in the range of (-100s, 1.734s).

Vacuum decay in the presence of a cosmic string

We study the false vacuum decay and bubble nucleation in the presence of a cosmic string in dS spacetime. A cosmic string induces a deficit angle in spacetime around itself so the nucleated bubble has the shape of a rugby ball. Working in thin wall approximation and using the junction conditions we study the dynamics of the bubble wall and calculate the Euclidean action. An interesting feature in our analysis is that the tension of the string is screened by the bubble such that an observer inside the bubble measures a different value of the tension than an outside observer. We show that the string can act as a catalyzer in which the nucleation rate is enhanced compared to the Coleman-de Luccia instanton. However, in general, the nucleation rate is not a monotonic function of the difference between the two tensions so in some regions of the parameters space the nucleation rate may be smaller than the Coleman-de Luccia bubble.

Induced fermionic vacuum polarization in a de Sitter spacetime with a compactified cosmic string

We study the fermionic condensate (FC) and the vacuum expectation value (VEV) of the energy-momentum tensor for a massive spinor field in the de Sitter (dS) spacetime including an ideal cosmic string. In addition, spatial dimension along the string is compactified to a circle of length $L$. The fermionic field is assumed to obey quasi-periodic condition along the $z$-axis. There are also magnetic fluxes running along the cosmic string and enclosed by the compact dimension. Both, the FC and the VEV of the energy-momentum tensor, are decomposed into two parts: one induced by the cosmic string in dS spacetime considering the absence of the compactification, and another one induced by the compactification. In particular, we show that the FC vanishes for a massless fermionic field.

Spherically symmetric black holes with electric and magnetic charge in extended gravity: physical properties, causal structure, and stability analysis in Einstein\u2019s and Jordan\u2019s frames

Novel static black hole solutions with electric and magnetic charges are derived for the class of modified gravities: f({{{mathcal {R}}}})={{{mathcal {R}}}}+2beta sqrt{{{mathcal {R}}}}, with or without a cosmological constant. The new black holes behave asymptotically as flat or (A)dS space-times with a dynamical value of the Ricci scalar given by R=frac{1}{r^2} and R=frac{8r^2Lambda +1}{r^2}, respectively. They are characterized by three parameters, namely their mass and electric and magnetic charges, and constitute black hole solutions different from those in Einstein’s general relativity. Their singularities are studied by obtaining the Kretschmann scalar and Ricci tensor, which shows a dependence on the parameter beta that is not permitted to be zero. A conformal transformation is used to display the black holes in Einstein’s frame and check if its physical behavior is changed w.r.t. the Jordan one. To this end, thermodynamical quantities, as the entropy, Hawking temperature, quasi-local energy, and the Gibbs free energy are calculated to investigate the thermal stability of the solutions. Also, the casual structure of the new black holes is studied, and a stability analysis is performed in both frames using the odd perturbations technique and the study of the geodesic deviation. It is concluded that, generically, there is coincidence of the physical properties of the novel black holes in both frames, although this turns not to be the case for the Hawking temperature.

Massive Rarita-Schwinger field in de Sitter space

We present a covariant quantization of the "massive" spin-${\frac{3}{2}}$ Rarita-Schwinger field in de Sitter (dS) spacetime. The dS group representation theory and its Wigner interpretation combined with the Wightman-G$\mbox{\"{a}}$rding axiomatic and analyticity requirements in the complexified pseudo-Riemanian manifold constitute the basis of the quantization scheme, while the whole procedure is carried out in terms of coordinate-independent dS plane waves. We make explicit the correspondence between unitary irreducible representations (UIRs) of the dS group and the field theory in dS spacetime: by "massive" is meant a field that carries a particular principal series representation of the dS group. We drive the plane-wave representation of the dS massive Rarita-Schwinger field in a manifestly dS-invariant manner. We show that it exactly reduces to its Minkowskian counterpart when the curvature tends to zero as far as the analyticity domain conveniently chosen. We then present the Wightman two-point function fulfilling the minimal requirements of local anticommutativity, covariance, and normal analyticity. The Hilbert space structure and the unsmeared field operator are also defined. The analyticity properties of the waves and the two-point function that we discuss in this paper allow for a detailed study of the Hilbert space of the theory, and give rise to the thermal physical interpretation.

On symmetry operators for the Maxwell equation on the Kerr-NUT-(A)dS spacetime

We focus on the method recently proposed by Lunin and Frolov–Krtouš–Kubizňák to solve the Maxwell equation on the Kerr-NUT-(A)dS spacetime by separation of variables. In their method, it is crucial that the background spacetime has hidden symmetries because they generate commuting symmetry operators with which the separation of variables can be achieved. In this work we reproduce these commuting symmetry operators in a covariant fashion. We first review the procedure known as the Eisenhart–Duval lift to construct commuting symmetry operators for given equations of motion. Then we apply this procedure to the Lunin–Frolov–Krtouš–Kubizňák (LFKK) equation. It is shown that the commuting symmetry operators obtained for the LFKK equation coincide with the ones previously obtained by Frolov–Krtouš–Kubizňák, up to first-order symmetry operators corresponding to Killing vector fields. We also address the Teukolsky equation on the Kerr-NUT-(A)dS spacetime and its symmetry operator is constructed.

Towards a Fisher-Information Description of Complexity in de Sitter Universe

Recent developments on holography and quantum information physics suggest that quantum information theory has come to play a fundamental role in understanding quantum gravity. Cosmology, on the other hand, plays a significant role in testing quantum gravity effects. How to apply this idea to a realistic universe is still unknown. Here, we show that some concepts in quantum information theory have cosmological descriptions. Particularly, we show that the complexity of a tensor network can be regarded as a Fisher information measure (FIM) of a dS universe, followed by several observations: (i) the holographic entanglement entropy has a tensor-network description and admits a information-theoretical interpretation, (ii) on-shell action of dS spacetime has a same description of FIM, (iii) complexity/action(CA) duality holds for dS spacetime. Our result is also valid for f ( R ) gravity, whose FIM exhibits the same features of a recent proposed L n norm complexity.