Blow-Up of Test Fields Near Cauchy Horizons

The behaviour of test fields near a compact Cauchy horizon is investigated. It is shown that solutions of nonlinear wave equations on Taub spacetime with generic initial data cannot be continued smoothly to both extensions of the spacetime through the Cauchy horizon. This is proved using an energy method. Similar results are obtained for the spacetimes of Moncrief containing a compact Cauchy horizon and for more general matter models.Comment: 10 pages, Plain TeX, MPA-AR-92-

Perturbations of Spatially Closed Bianchi III Spacetimes

Motivated by the recent interest in dynamical properties of topologically nontrivial spacetimes, we study linear perturbations of spatially closed Bianchi III vacuum spacetimes, whose spatial topology is the direct product of a higher genus surface and the circle. We first develop necessary mode functions, vectors, and tensors, and then perform separations of (perturbation) variables. The perturbation equations decouple in a way that is similar to but a generalization of those of the Regge--Wheeler spherically symmetric case. We further achieve a decoupling of each set of perturbation equations into gauge-dependent and independent parts, by which we obtain wave equations for the gauge-invariant variables. We then discuss choices of gauge and stability properties. Details of the compactification of Bianchi III manifolds and spacetimes are presented in an appendix. In the other appendices we study scalar field and electromagnetic equations on the same background to compare asymptotic properties.Comment: 61 pages, 1 figure, final version with minor corrections, to appear in Class. Quant. Gravi

Wormholes in spacetimes with cosmological horizons

A generalisation of the asymptotic wormhole boundary condition for the case of spacetimes with a cosmological horizon is proposed. In particular, we consider de Sitter spacetime with small cosmological constant. The wave functions selected by this proposal are exponentially damped in WKB approximation when the scale factor is large but still much smaller than the horizon size. In addition, they only include outgoing gravitational modes in the region beyond the horizon. We argue that these wave functions represent quantum wormholes and compute the local effective interactions induced by them in low-energy field theory. These effective interactions differ from those for flat spacetime in terms that explicitly depend on the cosmological constant.Comment: 10 pages, LaTeX 2.O9, no figure

Stability properties of black holes in self-gravitating nonlinear electrodynamics

We analyze the dynamical stability of black hole solutions in self-gravitating nonlinear electrodynamics with respect to arbitrary linear fluctuations of the metric and the electromagnetic field. In particular, we derive simple conditions on the electromagnetic Lagrangian which imply linear stability in the domain of outer communication. We show that these conditions hold for several of the regular black hole solutions found by Ayon-Beato and Garcia.Comment: 15 pages, no figure

Large Diffeomorphisms in (2+1)-Quantum Gravity on the Torus

The issue of how to deal with the modular transformations -- large diffeomorphisms -- in (2+1)-quantum gravity on the torus is discussed. I study the Chern-Simons/connection representation and show that the behavior of the modular transformations on the reduced configuration space is so bad that it is possible to rule out all finite dimensional unitary representations of the modular group on the Hilbert space of $L^2$-functions on the reduced configuration space. Furthermore, by assuming piecewise continuity for a dense subset of the vectors in any Hilbert space based on the space of complex valued functions on the reduced configuration space, it is shown that finite dimensional representations are excluded no matter what inner-product we define in this vector space. A brief discussion of the loop- and ADM-representations is also included.Comment: The proof for the nonexistence of the one- and two-dimensional representations of PSL(2,Z) in the relevant Hilbert space, has been extended to cover all finite dimensional unitary representations. The notation is slightly improved and a few references are added

Colliding Black Holes: The Close Limit

The problem of the mutual attraction and joining of two black holes is of importance as both a source of gravitational waves and as a testbed of numerical relativity. If the holes start out close enough that they are initially surrounded by a common horizon, the problem can be viewed as a perturbation of a single black hole. We take initial data due to Misner for close black holes, apply perturbation theory and evolve the data with the Zerilli equation. The computed gravitational radiation agrees with and extends the results of full numerical computations.Comment: 4 pages, Revtex, 3 postscript figures included, CGPG-94/2-

Numerical Investigation of Cosmological Singularities

Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te

Evidence for an oscillatory singularity in generic U(1) symmetric cosmologies on T3×RT^3 \times R

A longstanding conjecture by Belinskii, Lifshitz, and Khalatnikov that the singularity in generic gravitational collapse is locally oscillatory is tested numerically in vacuum, U(1) symmetric cosmological spacetimes on $T^3 \times R$. If the velocity term dominated (VTD) solution to Einstein's equations is substituted into the Hamiltonian for the full Einstein evolution equations, one term is found to grow exponentially. This generates a prediction that oscillatory behavior involving this term and another (which the VTD solution causes to decay exponentially) should be observed in the approach to the singularity. Numerical simulations strongly support this prediction.Comment: 15 pages, Revtex, includes 12 figures, psfig. High resolution versions of figures 7, 8, 9, and 11 may be obtained from anonymous ftp to ftp://vela.acs.oakland.edu/pub/berger/u1genfig

Supersymmetric quantum cosmology for Bianchi class A models

The canonical theory of (N=1) supergravity, with a matrix representation for the gravitino covector-spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.Comment: 10 pages, Revte

Perturbation theory for self-gravitating gauge fields I: The odd-parity sector

A gauge and coordinate invariant perturbation theory for self-gravitating non-Abelian gauge fields is developed and used to analyze local uniqueness and linear stability properties of non-Abelian equilibrium configurations. It is shown that all admissible stationary odd-parity excitations of the static and spherically symmetric Einstein-Yang-Mills soliton and black hole solutions have total angular momentum number $\ell = 1$, and are characterized by non-vanishing asymptotic flux integrals. Local uniqueness results with respect to non-Abelian perturbations are also established for the Schwarzschild and the Reissner-Nordstr\"om solutions, which, in addition, are shown to be linearly stable under dynamical Einstein-Yang-Mills perturbations. Finally, unstable modes with $\ell = 1$ are also excluded for the static and spherically symmetric non-Abelian solitons and black holes.Comment: 23 pages, revtex, no figure