Causally simple inextendible spacetimes are hole-free

It is shown that causally simple inextendible spacetimes are hole-free, thus confirming the expectation that causal simplicity removes holes from spacetime. This result is optimal in the sense that causal simplicity cannot be weakened to causal continuity. Physically, it means that if there is some partial Cauchy hypersurface which, for some reason, does not fully develop its influence, then there is some discontinuity in the causal relation.Comment: Revtex4, 9 pages. v2: minor correction

Quasistationary binary inspiral. I. Einstein equations for the two Killing vector spacetime

The geometry of two infinitely long lines of mass moving in a fixed circular orbit is considered as a toy model for the inspiral of a binary system of compact objects due to gravitational radiation. The two Killing fields in the toy model are used, according to a formalism introduced by Geroch, to describe the geometry entirely in terms of a set of tensor fields on the two-manifold of Killing vector orbits. Geroch's derivation of the Einstein equations in this formalism is streamlined and generalized. The explicit Einstein equations for the toy model spacetime are derived in terms of the degrees of freedom which remain after a particular choice of gauge.Comment: 37 pages, REVTeX, one PostScript Figure included with epsfig; minor formatting changes and copyright notice added for journal publicatio

The Topology of Branching Universes

The purpose of this paper is to survey the possible topologies of branching space-times, and, in particular, to refute the popular notion in the literature that a branching space-time requires a non-Hausdorff topology

Rigid Singularity Theorem in Globally Hyperbolic Spacetimes

We show the rigid singularity theorem, that is, a globally hyperbolic spacetime satisfying the strong energy condition and containing past trapped sets, either is timelike geodesically incomplete or splits isometrically as space $\times$ time. This result is related to Yau's Lorentzian splitting conjecture.Comment: 3 pages, uses revtex.sty, to appear in Physical Review

Quasi-Asimptotically Flat Spacetimes and Their ADM Mass

We define spacetimes that are asymptotically flat, except for a deficit solid angle $\alpha$, and present a definition of their ``ADM'' mass, which is finite for this class of spacetimes, and, in particular, coincides with the value of the parameter $M$ of the global monopole spacetime studied by Vilenkin and Barriola . Moreover, we show that the definition is coordinate independent, and explain why it can, in some cases, be negative.Comment: Late

The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion

We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of motion associated with the well known Geroch transformation, a functional $K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive in an open subset of the set of all $U(1)$-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate the constant of motion perturbatively for the Mixmaster spacetime and find it to be proportional to the minisuperspace Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly zero. Assuming that $K$ is exactly zero for the Mixmaster spacetime, we show that Geroch's transformation, when applied to the Mixmaster spacetime, gives a new \mbox{$U(1)$-symmetric} solution of the vacuum Einstein equations, globally defined on \mbox{$S^2 \times S^1 \times R$},which is non-homogeneous and presumably exhibits Mixmaster-like complicated dynamical behavior.Comment: 25 pages, preprint YCTP-20-93, Revte

No-horizon theorem for vacuum gravity with spacelike G1 isometry groups

We show that (3+1) vacuum spacetimes admitting a global, spacelike, one-parameter Lie group of isometries of translational type cannot contain apparent horizons. The only assumption made is that of the existence of a global spacelike Killing vector field with infinite open orbits; the four-dimensional vacuum spacetime metric is otherwise arbitrary. This result may thus be viewed as a hoop conjecture theorem for vacuum gravity with one spacelike translational Killing symmetry.Comment: 6 pages, revtex4; published in Phys. Rev. D Rapid Com

On the Causality and Stability of the Relativistic Diffusion Equation

This paper examines the mathematical properties of the relativistic diffusion equation. The peculiar solution which Hiscock and Lindblom identified as an instability is shown to emerge from an ill-posed initial value problem. These do not meet the mathematical conditions required for realistic physical problems and can not serve as an argument against the relativistic hydrodynamics of Landau and Lifshitz.Comment: 6 page

All conformally flat pure radiation metrics

The complete class of conformally flat, pure radiation metrics is given, generalising the metric recently given by Wils.Comment: 7 pages, plain Te

The Rest-Frame Instant Form of Relativistic Perfect Fluids and of Non-Dissipative Elastic Materials

For perfect fluids with equation of state $\rho = \rho (n,s)$, Brown gave an action principle depending only on their Lagrange coordinates $\alpha^i(x)$ without Clebsch potentials. After a reformulation on arbitrary spacelike hypersurfaces in Minkowski spacetime, the Wigner-covariant rest-frame instant form of these perfect fluids is given. Their Hamiltonian invariant mass can be given in closed form for the dust and the photon gas. The action for the coupling to tetrad gravity is given. Dixon's multipoles for the perfect fluids are studied on the rest-frame Wigner hyperplane. It is also shown that the same formalism can be applied to non-dissipative relativistic elastic materials described in terms of Lagrangian coordinates.Comment: revtex file, 70 page