Sitter Spacetime Research Articles

Time delay in κ-anti-de Sitter spacetime

Based on deformed translations in the κ-anti-de Sitter algebra, we derive a delay in the time of detection between a soft and a hard photon, which are simultaneously emitted at a distant event, to first order in the quantum gravity parameter. In the basis analyzed, the trajectories are undeformed, and the effect depends exclusively on the symmetry properties of the quantum algebra. The time delay depends linearly on the energy of the hard particle and has a sinusoidal dependence on the redshift of the source.

Symmetry and pseudosymmetry properties of Vaidya-Bonner-de Sitter spacetime

The primary focus of the current study is to explore the geometrical properties of the Vaidya-Bonner-de Sitter (briefly, VBdS) spacetime, which is a generalization of Vaidya-Bonner spacetime, Vaidya spacetime and Schwarzschild spacetime. In this study we have shown that the VBdS spacetime describes various types of pseudosymmetric structures, including pseudosymmetry due to conformal curvature, conharmonic curvature and other curvatures. Additionally, it is shown that such a spacetime is 2-quasi-Einstein, Einstein manifold of level 3, generalized Roter type, and that conformal 2-forms are recurrent. The geometric features of the Vaidya-Bonner spacetime, Vaidya spacetime, and Schwarzschild spacetime are obtained as a particular instance of the main determination. It is further established that the VBdS spacetime admits almost Ricci soliton and almost η-Yamabe soliton with respect to non-Killing vector fields. Also, it is proved that such a spacetime possesses generalized conharmonic curvature inheritance. It is interesting to note that in the VBdS spacetime the tensors Q(T,R), Q(S,R) and Q(g,R) are linearly dependent. Finally, this spacetime is compared with the Vaidya-Bonner spacetime with respect to their admitting geometric structures, viz., various kinds of symmetry and pseudosymmetry properties.

Hidden conformal symmetry and pair production near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter spacetime* *Supported by LPPM UNPAR under contract no. III/LPPM/2022-02/79-P

We show that the study of the hidden conformal symmetry that is associated with the Kerr/CFT correspondence can also apply to the cosmological horizon in the Kerr-Newman-Taub-NUT-de Sitter spacetime. This symmetry allows employing some two dimensional conformal field theory methods to understand the properties of the cosmological horizon. The entropy can be understood by using the Cardy formula, and the equation for the scattering process in the near region is in agreement with that obtained from a two point function in the two-dimensional conformal field theory. We also show that pair production can occur near the cosmological horizon in Kerr-Newman-Taub-NUT-de Sitter for near extremal conditions.

Anisotropic Strange Star Model Beyond Standard Maximum Mass Limit by Gravitational Decoupling in f(Q)$f(Q)$ Gravity

AbstractThe current theoretical development identified as the gravitational decoupling via Complete Geometric Deformation (CGD) method that has been introduced to explore the nonmetricity Q effects in relativistic astrophysics. In the present work, we have investigated the gravitationally decoupled anisotropic solutions for the strange stars in the framework of gravity by utilizing the CGD technique. To do this, we started with Tolman metric ansatz along with the MIT Bag model equation of state related to the hadronic matter. The solutions of the governing equations of motions are obtained by using two approaches, namely the mimicking of the θ sector to the seed radial pressure and energy density of the fluid model. The obtained models describe the self‐gravitating static, compact objects whose exterior solution can be given by the vacuum Schwarzschild Anti‐de Sitter spacetime. In particular, we modeled five stellar candidates, viz., LMC X‐4, PSR J1614‐2230, PSR J0740+6620, GW190814, and GW 170817 by using observational data. The rigorous viability tests of the solutions have been performed through regularity and stability conditions. We observed that the nonmetricity parameter and decoupling constant show a significant effect on stabilizing to ensure the physically realizable stellar models. The innovative feature of this work is to present the stable compact objects with masses beyond the without engaging of exotic matter. Therefore, the present study shows a new perception and physical significance about the exploration of ultra‐compact astrophysical objects.

Classification of Kerr–de Sitter-like spacetimes with conformally flat I in all dimensions

Using asymptotic characterization results of spacetimes at conformal infinity, we prove that Kerr-Schild-de Sitter spacetimes are in one-to-one correspondence with spacetimes in the Kerr-de Sitter-like class with conformally flat $\mathscr{I}$. Kerr-Schild-de Sitter are spacetimes of Kerr-Schild form with de Sitter background that solve the $(\Lambda>0)$-vacuum Einstein equations and admit a smooth conformal compactification sharing $\mathscr{I}$ with the background metric. Kerr-de Sitter-like metrics with conformally flat $\mathscr{I}$ are a generalization of the Kerr-de Sitter metrics, defined originally in four spacetime dimensions and extended here to all dimensions in terms of their initial data at null infinity. We explicitly construct all metrics in this class as limits or analytic extensions of Kerr-de Sitter. The structure of limits is inferred from corresponding limits of the asymptotic data, which appear to be hard to guess from the spacetime metrics.

Solenoid Configurations and Gravitational Free Energy of the AdS-Melvin Spacetime.

In this paper we explore a solenoid configuration involving a magnetic universe solution embedded in an empty Anti-de Sitter (AdS) spacetime. This requires a non-trivial surface current at the interface between the two spacetimes, which can be provided by a charged scalar field. When the interface is taken to the AdS boundary, we recover the full AdS–Melvin spacetime. The stability of the AdS–Melvin solution is also studied by computing the gravitational free energy from the Euclidean action.

Strong cosmic censorship in near-extremal Kerr-Sen-de Sitter spacetime

In this work, we first calculate equations of motion for particles in the Kerr-Sen-de Sitter black hole spacetime. Then, in the eikonal regime, we analytically obtain the quasi-normal resonant modes of massless neutral scalar field perturbation and find its imaginary part to be characterized by the surface gravity of a near-extremal Kerr-Sen-de Sitter black hole with the Cauchy horizon approaching the event horizon. We further show that the Penrose strong cosmic censorship conjecture is thus respected in this spacetime with dilaton scalar field and axion pseudoscalar field.

Vacuum fermionic currents in braneworld models on AdS bulk with a cosmic string

We investigate the effects of a brane and magnetic-flux-carrying cosmic string on the vacuum expectation value (VEV) of the current density for a charged fermionic field in the background geometry of (4+1)-dimensional anti-de Sitter (AdS) spacetime. The brane is parallel to the AdS boundary and the cosmic string is orthogonal to the brane. Two types of boundary conditions are considered on the brane that include the MIT bag boundary condition and the boundary conditions in Z2-symmetric braneworld models. The brane divides the space into two regions with different properties of the vacuum state. The only nonzero component of the current density is along the azimuthal direction and in both the regions the corresponding VEV is decomposed into the brane- free and brane-induced contributions. The latter vanishes on the string and near the string the total current is dominated by the brane-free part. At large distances from the string and in the region between the brane and AdS horizon the decay of the brane-induced current density, as a function of the proper distance, is power-law for both massless and massive fields. For a massive field this behavior is essentially different from that in the Minkowski bulk. In the region between the brane and AdS boundary the large-distance decay of the current density is exponential. Depending on the boundary condition on the brane, the brane-induced contribution is dominant or subdominant in the total current density at large distances from the string. By using the results for fields realizing two inequivalent irreducible representations of the Clifford algebra, the vacuum current density is investigated in C - and P -symmetric fermionic models. Applications are given for a cosmic string in the Randall-Sundrum-type braneworld model with a single brane.

Evolution of complexity for critical neutral Gauss-Bonnet-anti-de Sitter black holes

General Gauss-Bonnet gravity with a cosmological constant allows two anti-de Sitter (AdS) spacetimes to be taken as its vacuum solutions. It is found that there is a critical point in the parameter space where the two AdS vacuums coalesce into one, which is very different from the general Gauss-Bonnet gravity. Susskind’s team proposed a Complexity/Action duality based on AdS/CFT duality, which provides a new method of studying the complexity of black holes. Fan and Liang (Fan Z Y, Liang H Z 2019 <i>Phys. Rev. D</i> <b>100</b> 086016) gave the formula of the evolution of complexity for general higher derivative gravity, and discussed the complexity evolution of the neutral planar Gauss-Bonnet-AdS black holes in detail by the numerical method. With the method of studying the complexity of general higher derivative gravity proposed by Fan and Liang (2019), we investigate the complexity evolution of critical neutral Gauss-Bonnet-AdS black holes, and compare these results with the results of the general neutral Gauss-Bonnet-AdS black holes, showing that the overall regularities of the evolution of the complexity of these two objects are consistent, and their main difference lies in the dimensionless critical time. As for the five-dimensional critical neutral Gauss-Bonnet-AdS black holes, when the event horizon of the black holes is flat or spherical, the dimensionless critical times of black holes with different sizes are identical, all reaching their minimum values. While in the higher dimensional cases, the differences in dimensionless critical time among spherically symmetric critical neutral Gauss-Bonnet-AdS black holes with different sizes are obviously less than those of general ones. These differences are probably related to the criticality of the neutral Gauss-Bonnet-AdS black holes.

Uniqueness and nonexistence of complete spacelike hypersurfaces, Calabi–Bernstein type results and applications to Einstein–de Sitter and steady state type spacetimes

We investigate the geometry of complete spacelike hypersurfaces (immersed) in a generalized Robertson-Walker spacetime $$-I\times _fM^{n}$$ . Under suitable constraints on the sectional curvature of the Riemannian fiber $$M^n$$ , on the warping function f and on the future mean curvature (that is, the mean curvature function with respect to the future-pointing Gauss map of the spacelike hypersurface), we are able to prove that such a spacelike hypersurface must be a slice $$\{t\}\times M^{n}$$ of the ambient spacetime. Nonexistence and Calabi–Bernstein type results concerning entire spacelike graphs constructed over the Riemannian fiber $$M^n$$ are also obtained, as well as applications to the Einstein–de Sitter and steady state type spacetimes are given. Our approach is based on the so-called Omori–Yau’s generalized maximum principle and on certain integrability properties due to Yau.

Cosmological reconstruction and energy constraints in generalized Gauss\u2013Bonnet-scalar\u2013kinetic\u2013matter couplings

Recently introduced f(mathcal {G},T) theory is generalized by adding dependence on the arbitrary scalar field phi and its kinetic term (nabla phi )^2, to explore non-minimal interactions between geometry, scalar and matter fields in context of the Gauss–Bonnet theories. The field equations for the resulting fleft( mathcal {G},phi ,(nabla phi )^2,Tright) theory are obtained and show that particles follow non-geodesic trajectories in a perfect fluid surrounding. The energy conditions in the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime are discussed for the generic function fleft( mathcal {G},phi ,(nabla phi )^2,Tright) . As an application of the introduced extensions, using the reconstruction techniques we obtain functions that satisfy common cosmological models, along with the equations describing energy conditions for the reconstructed fleft( mathcal {G},phi ,(nabla phi )^2,Tright) gravity. The detailed discussion of the energy conditions for the de Sitter and power-law spacetimes is provided in terms of the fixed kinetic term i.e. in the fleft( mathcal {G},phi ,Tright) case. Moreover, in order to check viability of the reconstructed models, we discuss the energy conditions in the specific cases, namely the f(R,phi ,(nabla phi )^2) and f=gamma (phi ,X)mathcal {G}+mu T^{1/2} approaches. We show, that for the appropriate choice of parameters and constants, the energy conditions can be satisfied for the discussed scenarios.

Stability of asymmetric thin shell wormhole with a variable equation of state

Dynamical equations of asymmetric thin shell wormholes connecting two different spacetimes by applying the cut and paste technique are constructed. The linear stability with variable modified generalized Chaplygin gas (VMGCG) equation of state, where the pressure will be a function of both radius and density, is investigated. This formalism is applied to two specific cases of asymmetric wormhole of a Schwarzschild connected to Reissner–Nordström spacetime and Reissner–Nordström connected to Schwarzschild–De Sitter (SDS) spacetime.

Geometric Study of Marginally Trapped Surfaces in Space Forms and Robertson-Walker Spacetimes—An Overview

A marginally trapped surface in a spacetime is a Riemannian surface whose mean curvature vector is lightlike at every point. In this paper we give an up-to-date overview of the differential geometric study of these surfaces in Minkowski, de Sitter, anti-de Sitter and Robertson-Walker spacetimes. We give the general local descriptions proven by Anciaux and his coworkers as well as the known classifications of marginally trapped surfaces satisfying one of the following additional geometric conditions: having positive relative nullity, having parallel mean curvature vector field, having finite type Gauss map, being invariant under a one-parameter group of ambient isometries, being isotropic, being pseudo-umbilical. Finally, we provide examples of constant Gaussian curvature marginally trapped surfaces and state some open questions.

Induced energy-momentum tensor of a Dirac field in 2D de Sitter QED

We compute the expectation value of the energy-momentum tensor in the in-vacuum state of the quantized Dirac field coupled to a uniform electric field background on the Poincar$\rm\acute{e}$ path of the two dimensional de~Sitter spacetime ($\mathrm{dS}_{2}$). The adiabatic regularization scheme is applied to remove the ultraviolet divergencies from the expressions. We find, the off-diagonal components of the induced energy-momentum tensor vanishes and the absolute values of the diagonal components are increasing functions of the electric field which decrease as the Dirac field mass increases. We derive the trace anomaly of the induced energy-momentum tensor, which agrees precisely with the trace anomaly derived earlier in the literature. We have discusses the backreaction of the induced energy-momentum tensor on the gravitational field.

Thermodynamics for the k-essence emergent Reissner–Nordstrom–de Sitter spacetime

The {\bf k-}essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant $\L$ for certain configuration of {\bf k-}essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the {\bf k-}essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are negative for the RT type emergent black hole which implies that the system is thermodynamically unstable when the charge $Q\neq 0$ and the emergent spacetime is only dark energy dominated and it does not radiate when $Q=0$. The thermodynamically unstable situation is physically plausible only when we consider spin degrees of freedom of a system. We have made this analysis in the context of dark energy in an emergent gravity scenario having {\bf k-}essence scalar fields $\phi$ with a Dirac-Born-Infeld type lagrangian. The scalar field also satisfies the emergent equation of motion at $r\rightarrow\infty$.

Test fields cannot destroy extremal de Sitter black holes

We determine the timelike Killing vector field that gives the correct definition of energy for test fields propagating in a Kerr-Newman-de Sitter spacetime, and use this result to prove that test fields cannot destroy extremal Kerr-Newman-de Sitter black holes.

New black-string solutions for an anti–de Sitter brane in scalar-tensor gravity

We consider a five-dimensional theory with a scalar field non-minimally-coupled to gravity, and we look for novel black-string solutions in the bulk. By appropriately choosing the non-minimal coupling function of the scalar field, we analytically solve the gravitational and scalar-field equations in the bulk to produce black-string solutions that describe a Schwarzschild-Anti-de Sitter space-time on the brane. We produce two complete such solutions that are both characterised by a regular scalar field, a localised-close-to-our brane energy-momentum tensor and a negative-definite, non-trivial bulk potential that may support by itself the warping of the space-time even in the absence of the traditional, negative, bulk cosmological constant. Despite the infinitely-long string singularity in the bulk, the four-dimensional effective theory on the brane is robust with the effective gravity scale being related to the fundamental one and the warping scale. It is worth noting that if we set the mass of the black hole on the brane equal to zero, the black string disappears leaving behind a regular brane-world model with only a true singularity at the boundary of the fifth dimension.

Topological dyonic dilaton black holes in AdS spaces

We construct a new class of dyonic dilaton black hole solutions in the background of Anti-de Sitter (AdS) spacetime. In order to find an analytical solution which satisfy all the field equations, we should consider the string case where the dilaton coupling is $\alpha=1$. The asymptotic behaviour of the solution ($r\rightarrow\infty$) is exactly AdS, where the dilaton field becomes zero and the metric function reduces to $f(r)\rightarrow -\Lambda r^2/3$. In this spacetime, black hole horizons and cosmological horizons, can be a two-dimensional positive, zero or negative constant curvature surface. We study the physical properties of the solution and show that depending on the metric parameters, these solutions can describe black holes with one or two horizons or a naked singularity. We investigate thermodynamics of the solutions by calculating the charge, mass, temperature, entropy and the electric potential of these solutions and disclose that these conserved and thermodynamic quantities satisfy the first law of black hole thermodynamics. We also analyze thermal stability of the solutions and find the conditions for which we have a stable dyonic dilaton black hole.

A nonrelativistic limit for AdS perturbations

The familiar c → ∞ nonrelativistic limit converts the Klein-Gordon equation in Minkowski spacetime to the free Schrödinger equation, and the Einstein-massive-scalar system without a cosmological constant to the Schrödinger-Newton (SN) equation. In this paper, motivated by the problem of stability of Anti-de Sitter (AdS) spacetime, we examine how this limit is affected by the presence of a negative cosmological constant Λ. Assuming for consistency that the product Λc2 tends to a negative constant as c → ∞, we show that the corresponding nonrelativistic limit is given by the SN system with an external harmonic potential which we call the Schrödinger-Newton-Hooke (SNH) system. We then derive the resonant approximation which captures the dynamics of small amplitude spherically symmetric solutions of the SNH system. This resonant system turns out to be much simpler than its general-relativistic version, which makes it amenable to analytic methods. Specifically, in four spatial dimensions, we show that the resonant system possesses a three-dimensional invariant subspace on which the dynamics is completely integrable and hence can be solved exactly. The evolution of the two-lowest-mode initial data (an extensively studied case for the original general-relativistic system), in particular, is described by this family of solutions.

Character integral representation of zeta function in AdSd+1. Part I. Derivation of the general formula

The zeta function of an arbitrary field in (d + 1)-dimensional anti-de Sitter (AdS) spacetime is expressed as an integral transform of the corresponding so(2, d) representation character, thereby extending the results of [arXiv:1603.05387] for AdS4 and AdS5 to arbitrary dimensions. The integration in the variables associated with the so(d) part of the character can be recast into a more explicit form using derivatives. The explicit derivative expressions are presented for AdSd+1 with d = 2, 3, 4, 5, 6.