de Sitter spacetime and Bunch-Davies vacuum are a solution to the semiclassical Einstein-Schroedinger equations describing the evolution of spacetime geometry and a massive scalar quantum field with arbitrary coupling to curvature. The stability of this solution is proven by calculating the renormalized energy momentum tensor expectation value for small spatially homogeneous deviations from the de Sitter - Bunch-Davies system and solving the linearized backreaction problem. A renormalization scheme is developed. All momentum integrations are carried out analytically. The general solution is given in terms of its Laplace transform. It contains only two artificial instabilities: a constant gauge mode and an instability on the Planck time scale lying outside of the scope of our semiclassical theory.
In the framework of finite temperature conformal scalar field theory on de Sitter space-time the linearized Einstein equations for the renormalized stress tensor are exactly solved. In this theory quantum field fluctuations are concentrated near two spheres of the de Sitter radius, propagating as light wave fronts. Related cosmological aspects are shortly discussed. The analysis, performed for flat expanding universe, shows exponential damping of the back-reaction effects far from these spherical objects. The obtained solutions for the semiclassical Einstein equations in de Sitter background c…
A spatially flat Robertson-Walker spacetime driven by a cosmological constant is non-conformally coupled to a massless scalar field. The equations of semiclassical gravity are explicitly solved for this case, and a self-consistent de Sitter solution associated with the Bunch-Davies vacuum state is found (the effect of the quantum field is to shift slightly the effective cosmological constant). Furthermore, it is shown that the corrected de Sitter spacetime is stable under spatially-isotropic perturbations of the metric and the quantum state. These results are independent of the free renormaliz…
It is shown that the recent corpuscular description of gravity generically excludes de Sitter spacetime in any semiclassical version of f(R) gravity. A phantom phenomenology of the cosmic dynamics is also naturally excluded.
We present a method to semiclassically compute the pair creation rate of bosons and fermions in de Sitter spacetime. The results in the bosonic case agree with the ones in the literature. We find that for the constant electric field the fermionic and bosonic pair creation rate are the same. This analogy of bosons and fermions in the semiclassical limit is known from several flat spacetime examples.
I briefly review some of the recent progress in quantum field theory in curved spacetime and other aspects of semiclassical gravity, as reported at the D3 Workshop at GR15.
In a recent paper we investigated stationary, relativistic Bondi-type accretion in Schwarzschild-(anti-)de Sitter spacetimes. Here we study their stability, using the method developed by Moncrief. The analysis applies to perturbations satisfying the potential flow condition. We prove that global isothermal flows in Schwarzschild-anti-de Sitter spacetimes are stable, assuming the test-fluid approximation. Isothermal flows in Schwarzschild-de Sitter geometries and polytropic flows in Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter spacetimes can be stable, under suitable boundary condit…
In this paper we add a compact dimension to Schwarzschild-(anti-) de sitter and Kerr-(anti-) de sitter spacetimes, which describes (rotating) black string-(anti-) de sitter spacetime. We study the geodesic motion of test particles and light rays in this spacetime. We present the analytical solutions of the geodesic equations in terms of Weierstrass elliptic and Kleinian sigma hyperelliptical functions. We also discuss the possible orbits and classify them according to particle's energy and angular momentum. Moreover, the obtained results, are compared to Schwarzschild-(anti-) de sitter and Ker…
Modifying a method by Horowitz and Hubeny for asymptotically anti-de Sitter black holes, we establish the classical stability of the quasinormal modes of the de Sitter spacetime. Furthermore using a straightforward method we calculate the de Sitter quasinormal frequencies of the gravitational perturbations and discuss some properties of the radial functions of these quasinormal modes.
In the model of de Sitter gauge theory of gravity, the empty homogenous and isotropic spacetimes with constant curvature scalar and nonvanishing homogenous and isotropic torsion must have de Sitter metrics. The static de Sitter spacetime with static, O(3)-symmetric, vector torsion is the only spherically symmetric, vacuum solution with the metric of the form $g_{μν}={\rm diag}(A^2(r),-B^2(r),-r^2,-r^2\sin^2þ)$. The expressions of the torsion for different de Sitter spacetimes are presented. They are different from one to another. The properties of different de Sitter spacetimes with torsion ar…
In general, the Gibbons-Hawking temperature based on the Euclidean functional approach shows that de Sitter space in the Bunch-Davies vacuum is globally thermal. In the exactly soluble semiclassical Jackiw-Teitelboim model, we investigate thermal property of de Sitter space by taking into account the quantum back reaction of the geometry. The proper temperature of de Sitter space in the Bunch-Davies vacuum is found to vanish. In case of a certain quantum state breaking the de Sitter symmetry, de Sitter space can be made thermally exited; however, in this case the dilaton singularity cannot be …
The conformal structure of the Schwarzschild-de Sitter spacetime is analysed using the extended conformal Einstein field equations. To this end, initial data for an asymptotic initial value problem for the Schwarzschild-de Sitter spacetime is obtained. This initial data allows to understand the singular behaviour of the conformal structure at the asymptotic points where the horizons of the Schwarzschild-de Sitter spacetime meet the conformal boundary. Using the insights gained from the analysis of the Schwarzschild-de Sitter spacetime in a conformal Gaussian gauge, we consider nonlinear pertur…
Homogeneous isotropic models built in the framework of the Poincaré gauge theory of gravity (PGTG) based on general expression of gravitational Lagrangian without cosmological constant are analyzed. It is shown that the physical spacetime in the vacuum in the frame of PGTG can have the structure of flat de Sitter spacetime with torsion. Some physical consequences of obtained conclusion are discussed.
Recent observations in cosmology indicate an accelerating expansion of the universe postulated to arise from some form of dark energy, the paradigm being positive cosmological constant. De Sitter spacetime is the well-known isotropic solution to the Einstein equations with cosmological constant. However, as discussed here, it is not the most general, locally isotropic solution. One can construct an infinite family of such solutions, designer de Sitter spacetimes, which are everywhere locally isometric to a region of de Sitter spacetime. However, the global dynamics of these designer cosmologie…
We propose a definition of the accelerated frames in de Sitter spacetime whose metric recovers the Rindler approach in the flat limit. Unfortunately, this metric has no a satisfactory limit for vanishing acceleration such that its physical meaning remains obscure.
Equatorial motion of test particles in the Kerr-de Sitter spacetimes is considered. Circular orbits are determined, their properties are discussed for both the black-hole and naked-singularity spacetimes, and their relevance for thin accretion discs is established.
In the semiclassical limit of de Sitter gravity a separation of scales takes place that divides the theory into a "cosmic" sector and a "microscopic" sector. A similar separation takes place in the double-scaled limit of SYK theory. We examine the scaling behaviors that accompany these limits and find parallels that support the previously conjectured duality between Jackiw-Teitelboim gravity (with positive cosmological constant), and double-scaled SYK. This paper is a companion to "dS JT Gravity and Double-Scaled SYK" by Adel Rahman, to appear simultaneously with this paper.
We consider the linearized semiclassical Einstein equations for small deviations around de Sitter spacetime including the vacuum polarization effects of conformal fields. Employing the method of order reduction, we find the exact solutions for general metric perturbations (of scalar, vector and tensor type). Our exact (nonperturbative) solutions show clearly that in this case de Sitter is stable with respect to small metric deviations and a late-time attractor. Furthermore, they also reveal a breakdown of perturbative solutions for a sufficiently long evolution inside the horizon. Our results …
For there is always a wrong sign in the mass of graviton in the so-called perturbation expansion approximation of both Minkowski and de Sitter spacetimes, the existence of gravitational wave from the metric perturbation of de Sitter spacetime is doubtful. We try another way to start from the assumption that the gravitational wave equation should be both general covariant and conformal invariant and find that graviton is no longer a part of metric field, it has an effective mass of $m_g=\sqrt{R/6}=% \sqrt{2Λ/3}$ with correct sign in de Sitter spacetime, though it's intrinsic mass remains zero.
Within the general class of Asymptotically Anti-de Sitter spacetimes that are asymptotic to the A-de-S Schwarzschild metric, we give a simple positive mass theorem based on arguments from causal structure. A general result for all asymptotically A-de-S spacetimes will be given elsewhere.
It is shown how can be derived the normalized energy eigenspinors of the free Dirac field on anti-de Sitter spacetime, by using a Cartesian tetrad gauge where the separation of spherical variables can be done like in special relativity.
It is known that de Sitter spacetime can be seen as the solution of field equation for completely isotropic matter. In the present paper a new class of exact solutions in spherical symmetry is found and discussed, such that the energy--momentum tensor has two 2--dimensional distinct isotropic subspaces.
We analyze the scalar radiation emitted by a source in geodesic circular orbits around a Schwarzschild-de Sitter black hole. We obtain the emitted power using quantum field theory in curved spacetimes framework at tree level. We compare our results with the scalar synchrotron radiation in Schwarzschild spacetime.
Conformal rescaling of conformal Yano--Killing tensors and relations between Yano and CYK tensors are discussed. Pullback of these objects to a submanifold is used to construct all solutions of a CYK equation in anti-de Sitter and de Sitter spacetimes. Properties of asymptotic conformal Yano--Killing tensors are examined for asymptotic anti-de Sitter spacetimes. Explicit asymptotic forms of them are derived. The results are used to construct asymptotic charges in asymptotic AdS spacetime. Well known examples like Schwarzschild-AdS, Kerr-AdS and NUT-AdS are examined carefully in the constructio…
We study the thermodynamic properties of high dimensional Schwarzschild de Sitter spacetimes with the consideration of quantum effects. It is shown that by considering the cosmological constant as a variable state parameter and adding an extra term which denotes the vacuum energy, both the differential and integral mass formulas of the first law of Schwarzschild de Sitter spacetimes can be directly derived from the general Schwarzschild de Sitter metrics in a simple and natural way. Furthermore, after taking quantum effects into account, we can see that the cosmological constant must decrease …
We determine all spacetime flows which lead to a Hamiltonian dynamics in the space of general relativistic initial data sets with asymptotically Kerr-de Sitter ends. The corresponding Hamiltonians are calculated. Some implications for black-hole thermodynamics are pointed out.
Gaussian curvature of the two-surface r=0, t=const is calculated for the Kerr-de Sitter and Kerr-Newman-de Sitter solutions, yielding non-zero analytical expressions for both the cases. The results obtained, on the one hand, exclude the possibility for that surface to be a disk and, on the other hand, permit one to establish a correct geometrical interpretation of that surface for each of the two solutions.
We employ holographic duality to compute $\langle T_{μν} \rangle$ in strongly coupled $\mathcal N = 4$ supersymmetric Yang-Mills theory and then study evolution of the semiclassical Einstein field equations sourced by $\langle T_{μν} \rangle$. Linearizing about de Sitter space, we find that the semiclassical equations of motion reduce to a four dimensional scalar wave equation coupled to a five dimensional scalar wave equation. We compute the mode spectrum of these equations and find that there exists a critical value of the Hubble constant $H_c$ for which de Sitter space is unstable when $H <…
We consider the semiclassical Einstein equations (SEE) in the presence of a quantum scalar field with self-interaction $λϕ^4$. Working in the Hartree truncation of the two-particle irreducible (2PI) effective action, we compute the vacuum expectation value of the energy-momentum tensor of the scalar field, which act as a source of the SEE. We obtain the renormalized SEE by implementing a consistent renormalization procedure. We apply our results to find self-consistent de Sitter solutions to the SEE in situations with or without spontaneous breaking of the $Z_2$-symmetry.
The radiation spectrum of a classical charged particle (electron) moving in the de Sitter universe, has been calculated. The de Sitter metric is taken in the quasi-Euclidean Robertson-Walker form. It is shown that in the de Sitter spacetime an electron radiates as if it moved in a constant and homogeneous electric field with the strength vector E collinear to the electron momentum P.
We study a charged Taub-NUT spacetime solution in the DGP brane. We show that the Reissner-Nordstrom-Taub-NUT-de Sitter solution of Einstein-Maxwell gravity solves the corresponding equations of motion, where the cosmological constant is related to the cross-over scale in the DGP model. Following the approach by Teitelboim in discussing the thermodynamics of de Sitter spacetime and the proposal by Wu et al. for a conserved charge associated to the NUT parameter, we obtained the generalized Smarr mass formula and the first law of thermodynamics of the spacetime.
We present an expression for the Weyl-Weyl two-point function in de Sitter spacetime, based on a recently calculated covariant graviton two-point function with one gauge parameter. We find that the Weyl-Weyl two-point function falls off with distance like r^{-4}, where r is spacelike coordinate separation between the two points.
This paper has been withdrawn by the authors, an improved version with the title "Exact Fermi coordinates for a class of spacetimes", arXiv:0912.2779, replaces it.
We extensively study the exact solutions of the massless Dirac equation in 3D de Sitter spacetime that we published recently. Using the Newman-Penrose formalism, we find exact solutions of the equations of motion for the massless classical fields of spin s=1/2,1,2 and to the massive Dirac equation in 4D de Sitter metric. Employing these solutions, we analyze the absorption by the cosmological horizon and de Sitter quasinormal modes. We also comment on the results given by other authors.
We examine gravitational wave memory in the case where sources and detector are in an expanding cosmology. For simplicity, we treat the case where the cosmology is de Sitter spacetime, and discuss the possibility of generalizing our results to the case of a more realistic cosmology. We find results very similar to those of gravitational wave memory in an asymptotically flat spacetime, but with the magnitude of the effect multiplied by a redshift factor.
It is known that the extremal Reissner-Nordström black hole possesses a discrete conformal isometry that exchanges the black hole horizon with infinity. It is also known that the Reissner-Nordström-de Sitter spacetime posseses a similar discrete conformal isometry which exchanges the event horizon of the black hole with the cosmological horizon. In this short paper we will continue this line of thought and extend the conformal isometry of the latter spacetime and give an unphysical interpretation of the negative root.
The causal properties of the family of Kerr-de Sitter spacetimes are analyzed and compared to those of the Kerr family. At first we show that a Kerr-de Sitter spacetime can be viewed as an assembly of Carter's blocks i.e. four dimensional spacetime regions contained within Killing horizons or a Killing horizon and the asymptotic de Sitter region. From this perspective and leaving aside topological identifications, the causal properties of a Kerr de Sitter spacetime are determined by the causal properties of the individual Carter's blocks viewed as spacetimes in their own right. We show that an…
We introduce a calculation, based on purely topological reasoning, of the global equilibrium Hawking temperature of the Schwarzschild-de Sitter spacetime, where a Schwarzschild black hole horizon coexists with a de Sitter cosmological horizon. Our method is based on the careful calculation of the Euler characteristic of the total system, showing that this quantity completely determines the thermodynamical features of the system. The method is universal and can be applied to any structure possessing multiple horizons in general relativity.
We calculate the exact values of the quasinormal frequencies for an electromagnetic field and a gravitational perturbation moving in $D$-dimensional de Sitter spacetime ($D \geq 4$). We also study the quasinormal modes of a real massive scalar field and we compare our results with those of other references.
Trumpet geometries play an important role in numerical simulations of black hole spacetimes, which are usually performed under the assumption of asymptotic flatness. Our Universe is not asymptotically flat, however, which has motivated numerical studies of black holes in asymptotically de Sitter spacetimes. We derive analytical expressions for trumpet geometries in Schwarzschild-de Sitter spacetimes by first generalizing the static maximal trumpet slicing of the Schwarzschild spacetime to static constant mean curvature trumpet slicings of Schwarzschild-de Sitter spacetimes. We then switch to a…
We start a systematic investigation of possible isometries of the asymptotically de Sitter solutions to Einstein equations. We reformulate the Killing equation as conformal equations for the initial data at $\mathcal{I}^+$. This allows for partial classification of possible symmetry algebras. In particular, if they are not maximal, they may be at most $4$-dimensional. We provide several examples. As a simple collorary it is shown that the only spacetime in which the Killing horizon intersects $\mathcal{I}^+$ (after a conformal completion) is locally the de Sitter universe.
We study the decay of charged scalar and spinor fields around Reissner-Nordstrom black holes in de Sitter spacetime through calculations of quasinormal frequencies of the fields. The influence of the parameters of the black hole (charge, mass), of the decaying fields (charge, spin), and of the spacetime (cosmological constant) on the decay is analyzed. The analytic formula for calculation quasinormal frequencies for a large multipole number (eikonal approximation) is derived both for the spinor and scalar fieldss.
The conformal field equations are used to discuss the local existence of spherically symmetric solutions to the Einstein-Yang-Mills system which behave asymptotically like the anti-de Sitter spacetime. By using a gauge based on conformally privileged curves we obtain a formulation of the problem in terms of an initial boundary value problem on which a general class of maximally dissipative boundary conditions can be discussed. The relation between these boundary conditions and the notion of mass on asymptotically anti-de Sitter spacetimes is analysed.
We perform a Hadamard point-split renormalization of the current density $j_ν$ of a charged scalar field in a Reissner-Nordström-de Sitter spacetime. We compute numerically the expectation values of the components $j_r$ and $j_t$ in the Unruh state in the exterior region and study their dependence on the field parameters and the position.
The "twin paradox" of special relativity offers the possibility to make interstellar flights within a lifetime. For very long journeys with velocities close to the speed of light, however, we have to take into account the expansion of the universe. Inspired by the work of Rindler on hyperbolic motion in curved spacetime, we study the worldline of a uniformly accelerated observer in de Sitter spacetime and the communication between the traveling observer and an observer at rest.
We investigate the occurrence of naked singularities in the spherically symmetric, plane symmetric and cylindrically symmetric collapse of charged null fluid in an anti-de Sitter background. The naked singularities are found to be strong in Tipler's sense and thus violate the cosmic censorship conjecture, but not hoop conjecture.
Numerical arguments are presented for the existence of spherically symmetric regular and black hole solutions of the EYMH equations with a negative cosmological constant. These solutions approach asymptotically the anti-de Sitter spacetime. The main properties of the solutions and the differences with respect to the asymptotically flat case are discussed. The instability of the gravitating sphaleron solutions is also proven.
We describe two different, but equivalent semiclassical views of black hole physics in which the equivalence principle and unitarity are both accommodated. In one, unitarity is built-in, while the black hole interior emerges only effectively as a collective phenomenon involving horizon (and possibly other) degrees of freedom. In the other, more widely studied approach, the existence of the interior is manifest, while the unitarity of the underlying dynamics can be captured only indirectly by incorporating certain nonperturbative effects of gravity. These two pictures correspond to a distant de…
We compute the quantum string entropy S_s(m, H) from the microscopic string density of states of mass m in Anti de Sitter space-time. For high m, (high Hm -->c/α'), no phase transition occurs at the Anti de Sitter string temperature T_{s} which is higher than the flat space (Hagedorn) temperature t_{s}. (the Hubble constant H acts as producing a smaller string constant and thus, a higher tension). T_s is the precise quantum dual of the semiclassical (QFT) Anti de Sitter temperature scale . We compute the quantum string emission by a black hole in Anti de Sitter space-time (bhAdS). In the early…
We define the total energy-momenta for (4+1)-dimensional asymptotically anti-de Sitter spacetimes, and prove the positive energy theorem for such spacetimes.
