New varieties of Gowdy spacetimes

Gowdy spacetimes are generalized to admit two commuting spatial "local" Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston's geometries. Explicit spatial compactifications, as well as the boundary conditions for the metrics are given in a systematic way. A short comment on an implication to their dynamics toward the initial singularity is made.Comment: 13 pages with no figure. A reference added, and typos corrected. To appear in J.Math.Phy

Gauss-Bonnet black holes with non-constant curvature horizons

We investigate static and dynamical n(\ge 6)-dimensional black holes in Einstein-Gauss-Bonnet gravity of which horizons have the isometries of an (n-2)-dimensional Einstein space with a condition on its Weyl tensor originally given by Dotti and Gleiser. Defining a generalized Misner-Sharp quasi-local mass that satisfies the unified first law, we show that most of the properties of the quasi-local mass and the trapping horizon are shared with the case with horizons of constant curvature. It is shown that the Dotti-Gleiser solution is the unique vacuum solution if the warp factor on the (n-2)-dimensional Einstein space is non-constant. The quasi-local mass becomes constant for the Dotti-Gleiser black hole and satisfies the first law of the black-hole thermodynamics with its Wald entropy. In the non-negative curvature case with positive Gauss-Bonnet constant and zero cosmological constant, it is shown that the Dotti-Gleiser black hole is thermodynamically unstable. Even if it becomes locally stable for the non-zero cosmological constant, it cannot be globally stable for the positive cosmological constant.Comment: 15 pages, 1 figure; v2, discussion clarified and references added; v3, published version; v4, Eqs.(4.22)-(4.24) corrected, which do not change Eqs.(4.25)-(4.27

Dynamics of compact homogeneous universes

A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichm\"uller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four dimensional spacetime with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the spacetime isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogenoeus universes. Some examples are demonstrated for Bianchi II, VI${}_0$, VII${}_0$, and I universal covers.Comment: 32 pages with 2 figures (LaTeX with epsf macro package

Perfect fluid spheres with cosmological constant

We examine static perfect fluid spheres in the presence of a cosmological constant. New exact matter solutions are discussed which require the Nariai metric in the vacuum region. We generalize the Einstein static universe such that neither its energy density nor its pressure is constant throughout the spacetime. Using analytical techniques we derive conditions depending on the equation of state to locate the vanishing pressure surface. This surface can in general be located in regions with decreasing area group orbits. We use numerical methods to integrate the field equations for realistic equations of state and find consistent results.Comment: 15 pages, 6 figures; added new references, removed one figure, improved text, accepted for publication in PR

Cosmological Vorticity in a Gravity with Quadratic Order Curvature Couplings

We analyse the evolution of the rotational type cosmological perturbation in a gravity with general quadratic order gravitational coupling terms. The result is expressed independently of the generalized nature of the gravity theory, and is simply interpreted as a conservation of the angular momentum.Comment: 5 pages, revtex, no figure

Scattering of scalar perturbations with cosmological constant in low-energy and high-energy regimes

We study the absorption and scattering of massless scalar waves propagating in spherically symmetric spacetimes with dynamical cosmological constant both in low-energy and high-energy zones. In the former low-energy regime, we solve analytically the Regge-Wheeler wave equation and obtain an analytic absorption probability expression which varies with $M\sqrt{\Lambda}$, where $M$ is the central mass and $\Lambda$ is cosmological constant. The low-energy absorption probability, which is in the range of $[0, 0.986701]$, increases monotonically with increase in $\Lambda$. In the latter high-energy regime, the scalar particles adopt their geometric optics limit value. The trajectory equation with effective potential emerges and the analytic high-energy greybody factor, which is relevant with the area of classically accessible regime, also increases monotonically with increase in $\Lambda$, as long $\Lambda$ is less than or of the order of $10^4$. In this high-energy case, the null cosmological constant result reduces to the Schwarzschild value $27\pi r_g^2/4$.Comment: 12 pages, 6 figure

Regular black holes in an asymptotically de Sitter universe

A regular solution of the system of coupled equations of the nonlinear electrodynamics and gravity describing static and spherically-symmetric black holes in an asymptotically de Sitter universe is constructed and analyzed. Special emphasis is put on the degenerate configurations (when at least two horizons coincide) and their near horizon geometry. It is explicitly demonstrated that approximating the metric potentials in the region between the horizons by simple functions and making use of a limiting procedure one obtains the solutions constructed from maximally symmetric subspaces with different absolute values of radii. Topologically they are $AdS_{2}\times S^{2}$ for the cold black hole, $dS_{2}\times S^{2}$ when the event and cosmological horizon coincide, and the Pleba\'nski- Hacyan solution for the ultraextremal black hole. A physically interesting solution describing the lukewarm black holes is briefly analyze

Regular black holes with flux tube core

We consider a class of black holes for which the area of the two-dimensional spatial cross-section has a minimum on the horizon with respect to a quasiglobal (Krusckal-like) coordinate. If the horizon is regular, one can generate a tubelike counterpart of such a metric and smoothly glue it to a black hole region. The resulting composite space-time is globally regular, so all potential singuilarities under the horizon of the original metrics are removed. Such a space-time represents a black hole without an apparent horizon. It is essential that the matter should be non-vacuum in the outer region but vacuumlike in the inner one. As an example we consider the noninteracting mixture of vacuum fluid and matter with a linear equation of state and scalar phantom fields. This approach is extended to distorted metrics, with the requirement of spherical symmetry relaxed.Comment: 15 pages. 2 references adde

Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms

We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($\Lambda$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.Comment: 18 pages, no figure. accepted in Phys. Rev.

A simple proof of Birkhoff's theorem for cosmological constant

We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.Comment: 10 pages, 5 figures References added; typo in eqn. 12 fixe