Matching radiation-dominated and matter-dominated Einstein–de Sitter universes and an application for primordial black holes in evolving cosmological backgrounds

By matching across a surface of constant time, it is demonstrated that the spacetime for a radiation-dominated Einstein–de Sitter universe can be directly matched to the spacetime for a matter-dominated Einstein–de Sitter universe. Thus, this can serve as a model of a universe filled with radiation that suddenly is converted to matter and antimatter, or a universe filled with matter and antimatter that suddenly annihilates to leave radiation. This matching is shown to hold for asymptotically Einstein–de Sitter cosmological black hole spacetimes, yielding simplistic models of primordial black holes that evolve between being in radiation-dominated universes and matter-dominated universes.     

The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

The existence of the Carter constant in the Vaidya–Einstein–Kerr (VEK) spacetime and its relation to the Petrov type is investigated. This spacetime is an example of a black hole in an asymptotically non-flat background. We construct the Carter constant and obtain the Killing tensor in the VEK spacetime. The Newman–Penrose formalism is employed to obtain the spin coefficients. We present a complete (Petrov) classification of the VEK spacetime and the special case of the non-rotating Vaidya–Einstein–Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.     

Modified dispersion relations in Hořava–Lifshitz gravity and Finsler brane models

We study possible links between quantum gravity phenomenology encoding Lorentz violations as nonlinear dispersions, the Einstein–Finsler gravity models, EFG, and nonholonomic (non-integrable) deformations to Hořava–Lifshitz, HL, and/or Einstein’s general relativity, GR, theories. EFG and its scaling anisotropic versions formulated as Hořava–Finsler models, HF, are constructed as covariant metric compatible theories on (co) tangent bundle to Lorentz manifolds and respective anisotropic deformations. Such theories are integrable in general form and can be quantized following standard methods of deformation quantization, A-brane formalism and/or (perturbatively) as a nonholonomic gauge like model with bi-connection structure. There are natural warping/trapping mechanisms, defined by the maximal velocity of light and locally anisotropic gravitational interactions in a (pseudo) Finsler bulk spacetime, to four dimensional (pseudo) Riemannian spacetimes. In this approach, the HL theory and scenarios of recovering GR at large distances are generated by imposing nonholonomic constraints on the dynamics of HF, or EFG, fields.     

A New Parametrization for Tetrad Gravity

A new version of tetrad gravity in globally hyperbolic, asymptotically flat at spatial infinity spacetimes with Cauchy surfaces diffeomorphic to R ³ is obtained by using a new parametrization of arbitrary cotetrads to define a set of configurational variables to be used in the ADM metric action. Seven of the fourteen first class constraints have the form of the vanishing of canonical momenta. A comparison is made with other models of tetrad gravity and with the ADM canonical formalism for metric gravity.     

Fractional Dynamics from Einstein Gravity,General Solutions,and Black Holes

We study the fractional gravity for spacetimes with non-integer fractional derivatives. Our constructions are based on a formalism with the fractional Caputo derivative and integral calculus adapted to nonholonomic distributions. This allows us to define a fractional spacetime geometry with fundamental geometric/physical objects and a generalized tensor calculus all being similar to respective integer dimension constructions. Such models of fractional gravity mimic the Einstein gravity theory and various Lagrange–Finsler and Hamilton–Cartan generalizations in nonholonomic variables. The approach suggests a number of new implications for gravity and matter field theories with singular, stochastic, kinetic, fractal, memory etc processes. We prove that the fractional gravitational field equations can be integrated in very general forms following the anholonomic deformation method for constructing exact solutions. Finally, we study some examples of fractional black hole solutions, ellipsoid gravitational configurations and imbedding of such objects in solitonic backgrounds.     

Generic cosmic-censorship violation in anti-de Sitter space

We consider (four-dimensional) gravity coupled to a scalar field with potential V(phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti-de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.     

Solutions of higher dimensional Gauss–Bonnet FRW cosmology

We examine the effect on cosmological evolution of adding a Gauss–Bonnet term to the standard Einstein–Hilbert action for a (1 + 3) + d dimensional Friedman–Robertson–Walker (FRW) metric. By assuming that the additional dimensions compactify as a power law as the usual 3 spatial dimensions expand, we solve the resulting dynamical equations and find that the solution may be of either de Sitter or Kasner form depending upon whether the Gauss–Bonnet term or the Einstein term dominates.     

A Definition of Total Energy-Momenta and the Positive Mass Theorem on Asymptotically Hyperbolic 3-Manifolds. I

Two sets of asymptotically hyperbolic initial data are defined, which correspond to the spatial infinity in asymptotically AdS spacetimes and to the null infinity in asymptotically Minkowski spacetimes respectively. The positive mass theorem involving the total energy, the total linear momentum and the total angular momentum is established for these initial data sets.Research partially supported by National Natural Science Foundation of China under grant 10231050 and the innovation project of the Chinese Academy of Sciences.     

On cosmological mass with positive Λ

For asymptotically flat space-times, a very satisfactory expression for the total mass/energy of a system defined at future null infinity was provided by Bondi and Sachs, in the early 1960s. A generalization of this to space-times that are asymptotically de Sitter now has particular relevance in view of observational evidence, from 1998 onwards, indicating the presence of a positive cosmological constant Λ. In this article, some of the issues involved in such a definition are examined, showing that a somewhat different attitude to mass/energy must be taken, from that which was appropriate for asymptotically flat space-times. Two tentative suggestions are put forward for a retarded mass/energy definition with positive Λ, one based on a conformally invariant integral expression whose advanced time-derivative gives the Bondi–Sachs definition in the asymptotically flat case and the other, on the author’s 1982 approach to quasi-local energy. Such expressions could have some direct relevance to the proposal of Conformal Cyclic Cosmology, for which recent analysis of the CMB has provided some striking support.     

Einstein–Gauss–Bonnet black holes in de Sitter spacetime and the quasilocal formalism

We propose to compute the action and global charges of the asymptotically de Sitter solutions in Einstein–Gauss–Bonnet theory by using the counterterm method in conjunction with the quasilocal formalism. The general expression of the counterterms and the boundary stress tensor is presented for spacetimes of dimension d?7$d?7$. We apply this technique for several different solutions in Einstein–Gauss–Bonnet theory with a positive cosmological constant. Apart from known solutions, we consider also d=5$d=5$ vacuum rotating black holes with equal magnitude angular momenta. These solutions are constructed numerically within a nonperturbative approach, by directly solving the Einstein–Gauss–Bonnet equations with suitable boundary conditions.     

Unruh–DeWitt Detectors in Spherically Symmetric Dynamical Space-Times

In the present paper, Unruh–DeWitt detectors are used in order to investigate the issue of temperature associated with a spherically symmetric dynamical space-times. Firstly, we review the semi-classical tunneling method, then we introduce the Unruh–DeWitt detector approach. We show that for the generic static black hole case and the FRW de Sitter case, making use of peculiar Kodama trajectories, semiclassical and quantum field theoretic techniques give the same standard and well known thermal interpretation, with an associated temperature, corrected by appropriate Tolman factors. For a FRW space-time interpolating de Sitter space with the Einstein–de Sitter universe (that is a more realistic situation in the frame of ΛCDM cosmologies), we show that the detector response splits into a de Sitter contribution plus a fluctuating term containing no trace of Boltzmann-like factors, but rather describing the way thermal equilibrium is reached in the late time limit. As a consequence, and unlike the case of black holes, the identification of the dynamical surface gravity of a cosmological trapping horizon as an effective temperature parameter seems lost, at least for our co-moving simplified detectors. The possibility remains that a detector performing a proper motion along a Kodama trajectory may register something more, in which case the horizon surface gravity would be associated more likely to vacuum correlations than to particle creation.     

On the equivalence of the Einstein–Hilbert and the Einstein–Palatini formulations of general relativity for an arbitrary connection

In the framework of the Einstein–Palatini formalism, even though the projective transformation connecting the arbitrary connection with the Levi-Civita connection has been floating in the literature for a long time and perhaps the result was implicitly known in the affine gravity community, yet as far as we know Julia and Silva were the first to realise its gauge character. We rederive this result by using the Rosenfeld–Dirac–Bergmann approach to constrained Hamiltonian systems and do a comprehensive self contained analysis establishing the equivalence of the Einstein–Palatini and the metric formulations without having to impose the gauge choice that the connection is symmetric. We also make contact with the the Einstein–Cartan theory when the matter Lagrangian has fermions.     

Zero Modes of the Dirac Operator for Regular Einstein–Yang–Mills Background Fields

The existence of normalizable zero modes of the twisted Dirac operator is proven for a class of static Einstein–Yang–Mills background fields with a half-integer Chern–Simons number. The proof holds for any gauge group and applies to Dirac spinors in an arbitrary representation of the gauge group. The class of background fields contains all regular, asymptotically flat, CP-symmetric configurations with a connection that is globally described by a time-independent spatial one-form which vanishes sufficiently fast at infinity. A subset is provided by all neutral, spherically symmetric configurations which satisfy a certain genericity condition, and for which the gauge potential is purely magnetic with real magnetic amplitudes. Received: 19 March 1997 / Accepted: 21 April 1997     

Brane World Corrections to Newton’s Law

We discuss possible variations of the effective gravitational constant with length scale, predicted by most of alternative theories of gravity and unified models of physical interactions. After giving a brief general exposition, we review in more detail the predicted corrections to Newton’s law of gravity in diverse brane world models. We consider various configurations in 5 dimensions (flat, de Sitter and AdS branes in Einstein and Einstein–Gauss–Bonnet theories, with and without induced gravity and possible incomplete graviton localization), 5D multi-brane systems and some models in higher dimensions. A common feature of all models considered is the existence of corrections to Newton’s law at small radii comparable with the bulk characteristic length: at such radii, gravity on the brane becomes effectively multidimensional. Many models contain superlight perturbation modes, which modify gravity at large scale and may be important for astrophysics and cosmology.     

Mass,action, and entropy of Taub-Bolt-de Sitter spacetimes

We apply a recent proposal for defining conserved mass in asymptotically de Sitter spacetimes to the class of Taub-Bolt-de Sitter spacetimes. We compute the action, entropy, and conserved mass of these spacetimes, and find that in certain instances the mass and entropy can exceed that of pure de Sitter spacetime, in violation of recent suggestive conjectures to the contrary.     

Thermodynamics of Third Order Lovelock Anti-de Sitter Black Holes Revisited

We compute the mass and temperature of third order Lovelock black holes with negative Gauss-Bonnet coefficient α₂<0 in anti-de Sitter space and perform the stability analysis of topological black holes. When k=-1, the third order Lovelock black holes are thermodynamically stable for the whole range r₊. When k=1, we found that the black hole has an intermediate unstable phase for D=7. In eight dimensional spacetimes, however, a new phase of thermodynamically unstable small black holes appears if the coefficient \tilde{\alpha} is under a critical value.For D≧ 9, black holes have similar the distributions of thermodynamically stable regions to the case where the coefficient \tilde{\alpha} is under a critical value for D=8. It is worth to mention that all the thermodynamic and conserved quantities of the black holes with flat horizon do not depend on the Lovelock coefficients and are the same as those of black holes in general gravity.     

Arbitrary dimensional cosmological multi-black holes

We find cosmological black hole solutions for spacetimes of arbitrary dimension (greater than three) that are asymptotically de Sitter, and we show that these solutions can be extended to give multi-black hole solutions. We investigate the motion of a charged massive test particle in a five-dimensional extreme Reissner-Nordström de Sitter background. Furthermore we obtain Killing spinors for Reissner-Nordström de Sitter spacetimes. We also find five-dimensional cosmological black hole solutions in an asymptotically anti de Sitter spacetime and we show that these solutions are supersymmetric in the sense that they admit a supercovariantly constant spinor.     

Existence and Uniqueness Theorems for Massless Fields on a Class of Spacetimes with Closed Timelike Curves

We study the massless scalar field on asymptotically flat spacetimes with closed timelike curves (CTC’s), in which all future-directed CTC’s traverse one end of a handle (wormhole) and emerge from the other end at an earlier time. For a class of static geometries of this type, and for smooth initial data with all derivatives in L ₂ on ℐ ⁻ , we prove existence of smooth solutions which are regular at null and spatial infinity (have finite energy and finite L ₂ -norm) and have the given initial data on ℐ ⁻ . A restricted uniqueness theorem is obtained, applying to solutions that fall off in time at any fixed spatial position. For a complementary class of spacetimes in which CTC’s are confined to a compact region, we show that when solutions exist they are unique in regions exterior to the CTC’s. (We believe that more stringent uniqueness theorems hold, and that the present limitations are our own.) An extension of these results to Maxwell fields and massless spinor fields is sketched. Finally, we discuss a conjecture whose meaning is essentially that the Cauchy problem for free fields is well defined in the presence of CTC’s whenever the problem is well-posed in a geometric-optics limit. We provide some evidence in support of this conjecture, and we present counterexamples that show that neither existence nor uniqueness is guaranteed under weaker conditions. In particular, both existence and uniqueness can fail in smooth, asymptotically flat spacetimes with a compact nonchronal region. Received: 28 November 1994/Accepted: 20 May 1996