Under a weak assumption of the existence of a geodesic null congruence, we present the general solution of the Einstein field equations in three dimensions with any value of the cosmological constant, admitting an aligned null matter field, and also gyratons (a matter field in the form of a null dust with an additional internal spin). The general local solution consists of the expanding Robinson-Trautman class and the non-expanding Kundt class. The gyratonic solutions reduce to spacetimes with a pure radiation matter field when the spin is set to zero. Without matter fields, we obtain new forms of the maximally symmetric vacuum solutions. We discuss these complete classes of solutions and their various subclasses. In particular, we identify the gravitational field of an arbitrarily accelerating source (the Kinnersley photon rocket, which reduces to a Vaidya-type non-moving object) in the Robinson-Trautman class, and pp-waves, vanishing scalar invariants (VSI) spacetimes, and constant scalar invariants (CSI) spacetimes in the Kundt class.
The metric ansatz is used to describe the gravitational field of a beam-pulse of spinning radiation (gyraton) in an arbitrary number of spacetime dimensions D. First we demonstrate that this metric belongs to the class of metrics for which all scalar invariants constructed from the curvature and its covariant derivatives vanish. Next, it is shown that the vacuum Einstein equations reduce to two linear problems in (D-2)-dimensional Euclidean space. The first is to find the static magnetic potential created by a point-like source. The second requires finding the electric potential created by a p…
We present and analyze exact solutions of the Einstein-Maxwell equations in higher dimensions which form a large subclass of the Kundt family of spacetimes. We assume that the cosmological constant may be nonvanishing, and the matter consists of a background aligned electromagnetic field and an additional pure radiation (gyratonic) field with a spin. We show that the field equations reduce to a set of linear equations on the transverse space which can be solved exactly and expressed in terms of the Green functions. We thus find explicit exact gyratonic gravitational and electromagnetic fields …
We present and analyze exact gyraton and nonexpanding gravitational wave solutions of algebraic type II on backgrounds which are a direct-product of two 2-spaces of constant curvature, or more general type D spacetimes. This family of electro-vacuum background spacetimes contains the Nariai, anti-Nariai and Plebanski-Hacyan universes, conformally flat Bertotti-Robinson and Minkowski spaces. The gyraton solutions are given in a simple Kundt metric form. They belong to the recently discussed class of spacetimes with constant scalar invariants (CSI) of the curvature tensor. We show that the Einst…
We systematically investigate the complete class of vacuum solutions in the Einstein-Gauss-Bonnet gravity theory which belong to the Kundt family of non-expanding, shear-free and twist-free geometries (without gyratonic matter terms) in any dimension. The field equations are explicitly derived and simplified, and their solutions classified into three distinct subfamilies. Algebraic structures of the Weyl and Ricci curvature tensors are determined. The corresponding curvature scalars directly enter the invariant form of equation of geodesic deviation, enabling us to understand the specific loca…
The Gauss-Bonnet gravity is a special case of so-called Quadratic Gravity, which is an extension of Einstein's theory with additional terms in action that are quadratic combinations of the Riemann tensor and its contractions. These corrections are needed, for example, in perturbative quantum gravity. We consider the family of Kundt spacetimes, which is defined in a purely geometrical way by admitting a shear-free, twist-free and expansion-free null geodesic congruence. In particular, we focus on the Kundt solutions without gyratonic terms, and we investigate the constraints imposed by the Eins…
We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subc…
Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the gravitational field can be naturally decomposed into Newton-type tidal effects typical for type II spacetimes, longitudinal deformations mainly present in spacetimes of algebraic type III, and type N purely transverse effects corresponding to gravitational waves with D(D-3)/2 independent polarization states. We explicitly study the most important examples, namely exac…
In this paper the Seiberg-Witten map is first analyzed for non-commutative Yang-Mills theories with the related methods, developed in the literature, for its explicit construction, that hold for any gauge group. These are exploited to write down the second-order Seiberg-Witten map for pure gravity with a constant non-commutativity tensor. In the analysis of pure gravity when the classical space-time solves the vacuum Einstein equations, we find for three distinct vacuum solutions that the corresponding non-commutative field equations do not have solution to first order in non-commutativity, wh…
We study pure Lovelock vacuum and perfect fluid equations for Kasner-type metrics. These equations correspond to a single $N$th order Lovelock term in the action in $d=2N+1,\,2N+2$ dimensions, and they capture the relevant gravitational dynamics when aproaching the big-bang singularity within the Lovelock family of theories. Pure Lovelock gravity also bears out the general feature that vacuum in the critical odd dimension, $d=2N+1$, is kinematic; i.e. we may define an analogue Lovelock-Riemann tensor that vanishes in vacuum for $d=2N+1$, yet the Riemann curvature is non-zero. We completely cla…
It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a normal and timelike congruence of observers.
We find a new exact $Λ$-vacuum solution in pure Gauss-Bonnet gravity with NUT charge in six dimension with horizon having product topology $S^{(2)} \times S^{(2)}$. We also discuss its horizon and singularity structure, and consequently arrive at a parameter window for its physical viability. It should be noted that all NUT black hole solutions in higher dimensions have product, instead of spherical, topology. We prove, in general, that it is because of the radial symmetry of the NUT spacetime; i.e. in higher dimensions NUT spacetime cannot maintain radial symmetry unless horizon has $S^{(2)}$…
We re-examine vacuum polarisation of a scalar field in a quasi-local volume including the horizon. We find that Hawking radiation rate is derived as a pure decay of vacuum due to scalar field interaction with classical gravity exactly in the same way as the origin of vacuum polarisation effect in Electrodynamics.
In this paper we investigate the vacuum polarization effects associated with a massive quantum scalar field in de Sitter spacetime in the presence of gravitational topological defects. Specifically we calculate the vacuum expectation value of the field square, $<Φ^2>$. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the defects.
In this paper, we introduce higher dimensional thin-shell wormholes in pure Gauss-Bonnet gravity. The focus is on thin-shell wormholes constructed by $N\geq5$-dimensional spherically symmetric vacuum solutions. The results suggest that, under certain conditions, it is possible to have thin-shell wormholes that both satisfy the weak energy condition and be stable against radial perturbations.
We analyse vacuum decay in rotating BTZ black hole spacetimes with the thin wall approximation. Possible parameter regions for the vacuum decay are clarified. We find that the nucleation rate is dominated by the bounce solution with the static shell configuration. The nucleation rate of the static shell decreases with the mass of the initial black hole. For a larger/smaller value of the initial black hole, the nucleation rate can be smaller/larger than that of the Coleman De Luccia vacuum decay in the pure AdS spacetime. Through the vacuum decay, the black hole gains its mass and loses the hor…
We discuss an ${\cal R}+{\cal R}^n$ class of modified ${\cal N}=1$, D=4 supergravity models where the deformation is a monomial ${\cal R}^n\big|_F$ in the chiral scalar curvature multiplet ${\cal R}$ of the "old minimal" auxiliary field formulation. The scalaron and goldstino multiplets are dual to each other in this theory. Since one of them is not dynamical, this theory, as recently shown, cannot be used as the supersymmetric completion of $R+R^n$ gravity. This is confirmed by investigating the scalar potential and its critical points in the dual standard supergravity formulation with a sing…
We introduce a $(5+m)$-dimensional vacuum description of five-dimensional bulk inflaton models with exponential potentials that makes analysis of cosmological perturbations simple and transparent. We show that various solutions, including the power-law inflation model recently discovered by Koyama and Takahashi, are generated from known $(5+m)$-dimensional vacuum solutions of pure gravity. We derive master equations for all types of perturbations, and each of them becomes a second order differential equation for one master variable supplemented by simple boundary conditions on the brane. One e…
We argue that part of "dark matter" is not made of matter, but of the singular world-surfaces in the solutions of Einstein's vacuum field equation G_{μν}=0. Their Einstein-Hilbert action governs also their quantum fluctuation. It coincides with the action of closed bosonic "strings" in four spacetime dimensions, which appear here in a new physical context. Thus, part of dark matter is of a purely geometric nature, and its quantum physics is governed by the same string theory, whose massless spin-2 particles interact like the quanta of Einstein's theory.
We study dynamical structure of Pure Lovelock gravity in spacetime dimensions higher than four using the Hamiltonian formalism. The action consists of cosmological constant and a single higher-order polynomial in the Riemann tensor. Similarly to Einstein-Hilbert action, it possesses a unique constant curvature vacuum and charged black hole solutions. We analyze physical degrees of freedom and local symmetries in this theory. In contrast to the Einstein-Hilbert case, a number of degrees of freedom depends on the background and can vary from zero to the maximal value carried by the Lovelock theo…
We obtain rotating black hole metric for higher dimensional Einstein and pure Lovelock gravity by employing two independent and well motivated methods. One is based on the principle of incorporation of Newtonian acceleration for timelike motion while no acceleration for null motion. The other is the well known Newman-Janis alogrithm that converts a static black hole into a rotating one through a complex transformation. It turns out that both the methods give the same metric which for Einst of the eour pure Lovelock metricein black hole is an exact vacuum solution while for pure Lovelock black …
Positive frequency Wightman function and vacuum expectation values of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter and satisfying Robin boundary condition on a uniformly accelerated infinite plate. The both regions of the right Rindler wedge, (i) on the right (RR region) and (ii) on the left (RL region) of the plate are investigated. For the case (ii) the electromagnetic field is considered as well. The mode summation method is used with combination of a variant of the generalized Abel-Plana formula. This allows to present the exp…
It is shown that there are no vacuum space-times (with or without cosmological constant) for which the Weyl-tensor is purely gravito-magnetic with respect to a congruence of freely falling observers.
Spacetimes in which the electric part of the Weyl tensor vanishes (relative to some timelike unit vector field) are said to be purely magnetic. Examples of purely magnetic spacetimes are known and are relatively easy to construct, if no restrictions are placed on the energy-momentum tensor. However it has long been conjectured that purely magnetic vacuum spacetimes (with or without a cosmological constant) do not exist. The history of this conjecture is reviewed and some advances made in the last year are described briefly. A generalisation of this conjecture first suggested for type D vacuum …
In open quantum systems, we study the geometric phases acquired for a two-level atom coupled to a bath of fluctuating vacuum massless scalar fields due to linear acceleration and circular motion without and with a boundary. In free space, as we amplify acceleration, the geometric phase acquired purely due to linear acceleration case firstly is smaller than the circular acceleration case in the ultrarelativistic limit for the initial atomic state $θ\in(0,\fracπ{2})\cup(\fracπ{2},π)$, then equals to the circular acceleration case in a certain acceleration, and finally, is larger than the circula…
We present a simple general proof that Casimir force cannot originate from the vacuum energy of electromagnetic (EM) field. The full QED Hamiltonian consists of 3 terms: the pure electromagnetic term $H_{\rm em}$, the pure matter term $H_{\rm matt}$ and the interaction term $H_{\rm int}$. The $H_{\rm em}$-term commutes with all matter fields because it does not have any explicit dependence on matter fields. As a consequence, $H_{\rm em}$ cannot generate any forces on matter. Since it is precisely this term that generates the vacuum energy of EM field, it follows that the vacuum energy does not…
It is well known that the vacuum in the Einstein gravity, which is linear in the Riemann curvature, is trivial in the critical (2+1=3) dimension because vacuum solution is flat. It turns out that this is true in general for any odd critical $d=2n+1$ dimension where $n$ is the degree of homogeneous polynomial in Riemann defining its higher order analogue whose trace is the nth order Lovelock polynomial. This is the "curvature" for nth order pure Lovelock gravity as the trace of its Bianchi derivative gives the corresponding analogue of the Einstein tensor \cite{bianchi}. Thus the vacuum in the …
We show that there are no vacuum solutions with a purely magnetic Weyl tensor with respect to an observer submitted to kinematic restrictions involving first order differential scalars. This result generalizes previous ones for the vorticity-free and shear-free cases. We use a covariant approach which makes evident that only the Bianchi identities are used and, consequently, the results are also valid for non vacuum solutions with vanishing Cotton tensor.
Under the action of the Geroch group, the Minkowski metric can be transformed into any vacuum metric with two commuting Killing vectors. In principle, this reduces the problem of deriving vacuum metrics with two commuting Killing vectors to pure algebra. In this short note, we use these facts to give a purely algebraic derivation of the Einstein-Rosen metric, which describes a cylindrical gravitational wave. Our derivation has a straightforward extension to gravitational pulse waves.
In this paper we investigate the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor associated with a massive scalar quantum field induced by a generalized cosmic string in D-dimensional anti-de Sitter (AdS) spacetime. In order to develop this analysis we evaluate the corresponding Wightman function. As we shall observe, this function is expressed as the sum of two terms: the first one corresponds to the Wightman function in pure AdS bulk and the second one is induced by the presence of the string. The second contribution is finite at coincidence limit and is …
We review explicit solutions to the stationary axisymmetric Einstein-Maxwell equations which can be interpreted as disks of charged dust. The disks of finite or infinite extension are infinitesimally thin and constitute a surface layer at the boundary of an electro-vacuum. The Einstein-Maxwell equations in the presence of one Killing vector are obtained by using a projection formalism. The SU(2,1) invariance of the stationary Einstein-Maxwell equations can be used to construct solutions for the electro-vacuum from solutions to the pure vacuum case via a so-called Harrison transformation. It is…
An earlier construction by the authors of sequences of globally regular, asymptotically flat initial data for the Einstein vacuum equations containing trapped surfaces for large values of the parameter is extended, from the time symmetric case considered previously, to the case of maximal slices. The resulting theorem shows rigorously that there exists a large class of initial configurations for non-time symmetric pure gravitational waves satisfying the assumptions of the Penrose singularity theorem and so must have a singularity to the future.
We investigate, in the context of five-dimensional (5D) Brans-Dicke theory of gravity, the idea that macroscopic matter configurations can be generated from pure vacuum in five dimensions, an approach first proposed in the framework of general relativity. We show that the 5D Brans-Dicke vacuum equations when reduced to four dimensions lead to a modified version of Brans-Dicke theory in four dimensions (4D). As an application of the formalism, we obtain two five-dimensional extensions of four-dimensional O'Hanlon and Tupper vacuum solution and show that they lead two different cosmological scen…
We exhibit large classes of local actions for the vacuum Einstein equations. In presence of fermions, or more generally of matter which couple to the connection, these actions lead to inequivalent equations revealing an arbitrary number of parameters. Even in the pure gravitational sector, any corresponding quantum theory would depend on these parameters.
In the `condensed phase' of effective quantum field theories one expects deviations from exact Lorentz invariance at ultralow momenta | k| < delta where the shell 'delta' should only vanish in the strict local limit of the theory when the ultraviolet cutoff 'Lambda' tends to infinity. I explore this idea for the Higgs condensate suggesting that, in this case, the resulting relation connecting 'delta', 'Lambda' and the Fermi scale might provide a simple physical solution of the `hierarchy problem'. In this picture, the Planck scale is not a purely ultraviolet quantity but embodies in its numeri…
An existence and stability result for a class of purely radiative vacuum spacetimes arising from hyperboloidal data is given. This result generalises semiglobal existence results for Minkowski-like spacetimes to the case where the reference solution contains gravitational radiation. The analysis makes use of the extended conformal field equations and a gauge based on conformal geodesics so that the location and structure of the conformal boundary of the perturbed solutions is known a priori.
The well-known treatment of asymptotically flat vacuum fields is adapted to pure radiation fields. In this approach we find a natural normalization of the radiation null vector. The energy balance at null infinity shows that the mass loss results from a linear superposition of the pure and the gravitational radiation parts. By transformation to Bondi-Sachs coordinates the Kinnersley photon rocket is found to be the only axisymmetric Robinson-Trautman pure radiation solution without gravitational radiation.
In an earlier paper [6] the author wrote the homothetic equations for vacuum solutions in a first order formalism allowing for arbitrary alignment of the dyad. This paper generalises that method to homothetic equations in non-vacuum spaces and also provides useful second integrability conditions. An application to the well-known Petrov type O pure radiation solutions is given.
We discuss tests of the Einstein Equivalence Principle due to energies which are purely quantum mechanical in origin. In particular, we consider using Lamb Shift energies to test for possible quantum violations of Local Position Invariance. (to appear in the Proceedings of the 5th Canadian Conference on General Relativity and Relativistic Astrophysics, University of Waterloo, May 13-- 15, 1993) (acknowledgements changed to correct an omission in the originally submitted version)
It is well known that vacuum equation of arbitrary Lovelock order for static spacetime ultimately reduces to a single algebraic equation, we show that the same continues to hold true for pure Lovelock gravity of arbitrary order $N$ for topology ${\bf S^{(n)} \times S^{(n)}}$. We thus obtain pure Lovelock static black hole solutions with two-sphere topology for any order $N$, and in particular we study in full detail the third and fourth order Lovelock black holes. It is remarkable that thermodynamical stability of black hole discerns between odd and even $N$, and consequently between negative …
The product spacetimes of constant curvature describe in Einstein gravity, which is linear in Riemann curvature, Nariai metric which is a solution of $Λ$-vacuum when curvatures are equal, $k_1=k_2$, while it is Bertotti-Robinson metric describing uniform electric field when curvatures are equal and opposite, $k_1=-k_2$. We probe pure Lovelock gravity by these simple product spacetimes and prove that the same characterization of these solutions is indeed true in general for pure Lovelock gravitational equation of order $N$ in $d=2N+2$ dimension. We also consider these solutions for the conventi…
We propose a novel cosmological scenario with the space-time emerging from a pure initial de Sitter stage and subsequently evolving into the radiation, matter and dark energy dominated epochs, thereby avoiding the initial singularity and providing a complete description of the expansion history and a natural solution to the horizon problem. The model is based on a dynamical vacuum energy density which evolves as a power series of the Hubble rate. The transit from the inflation into the standard radiation epoch is universal, giving a clue for a successful description of the graceful exit. Since…
We prove that smooth asymptotically flat solutions to the Einstein vacuum equations which are assumed to be periodic in time, are in fact stationary in a neighborhood of infinity. Our result applies under physically relevant regularity assumptions purely at the level of the initial data. In particular, our work removes the assumption of analyticity up to null infinity in [Bicak, Scholtz, and Tod; 2010]. The proof relies on extending a suitably constructed "candidate" Killing vector field from null infinity, via Carleman-type estimates obtained in [Alexakis, Schlue, Shao; 2013].
We analyze a toy model describing an empty spacetime in which the motion of a test mass (and the trajectories of photons) evidence the presence of a continuous and homogeneous distribution of matter; however, since the energy-momentum tensor vanishes, no real matter or energy distribution is present at all. Thus, a hypothetical observer will conclude that he is immersed in some sort of dark matter, even though he has no chance to directly detect it. This suggests yet another possibility of explaining the elusive dark matter as a purely dynamical effect due to the curvature of spacetime.
We focus on the Penrose's Weyl Curvature Hypothesis in a general framework encompassing many specific models discussed in literature. We introduce a candidate density for the Weyl entropy in pure spacetime perfect fluid regions and show that it is monotonically increasing in time under very general assumptions. Then we consider the behavior of the Weyl entropy of compact regions, which is shown to be monotone in time as well under suitable hypotheses, and also maximal in correspondence with vacuum static metrics. The minimal entropy case is discussed too.
