Bounds for scalar waves on self-similar naked-singularity backgrounds

The stability of naked singularities in self-similar collapse is probed using scalar waves. It is shown that the multipoles of a minimally coupled massless scalar field propagating on a spherically symmetric self-similar background spacetime admitting a naked singularity maintain finite $L^2$ norm as they impinge on the Cauchy horizon. It is also shown that each multipole obeys a pointwise bound at the horizon, as does its locally observed energy density. $L^2$ and pointwise bounds are also obtained for the multipoles of a minimally coupled massive scalar wave packet.Comment: 16 pages, 1 figure. Published versio

An Analysis of Wave Tails based on the Geometric Optics Approximation

The effect of the existence of tails on the propagation of scalar waves in curved space-time is considered via an analysis of flux integrals of the energy-stress-momentum tensor of the waves. The geometric optics approximation is formulated in terms of such flux integrals, and three examples are investigated in detail in order to determine the possible effects of wave tails. The approximation is valid for waves in Minkowski space-time (tail-free) and waves in Schwarzschild space-time (weak tails) but it is shown how the approximation can break down in a cosmological scenario due to destructive interference by strong tails. In this last situation, the waves do not radiate.Comment: 21 pages, plain latex replaces revtex version. One figure, hard copy available on request from autho

The Goldberg--Kerr Approach to Lorentz Covariant Gravity

The approach to asymptotic electromagnetic fields introduced by Goldberg and Kerr is used to study various aspects of Lorentz Covariant Gravity. Retarded multipole moments of the source, the central objects of this study, are defined, and a sequence of conservation equations for these are derived. These equations are used extensively throughout the paper. The solution of the linearized Einstein equation is obtained in terms of the retarded moments for a general bound source, correct to $O(r^{-4})$. This is used to obtain the peeling--off of the linearized field, and to study the geometric optics approximation for the field and for the energy-momentum pseudotensor of the field. It is shown that the energy-momentum 4-vector splits into the `total radiated 4-momentum' and the `bound 4-momentum of the source', similar to the case of the electromagnetic field. In the case of a source which has only retarded pole, dipole and quadrupole moments, a decomposition into arbitrary functions of a null coordinate is obtained which allows comparison with the solutions for linearized gravity obtained by other authors.Comment: 28 pages, revtex, uuencode

Particle and photon orbits in McVittie spacetimes

McVittie spacetimes represent an embedding of the Schwarzschild field in isotropic cosmological backgrounds. Depending on the scale factor of the background, the resulting spacetime may contain black and white hole horizons, as well as other interesting boundary features. In order to further clarify the nature of these spacetimes, we address this question: do there exist bound particle and photon orbits in McVittie spacetimes? Considering first circular photon orbits, we obtain an explicit characterization of all McVittie spacetimes for which such orbits exist: there is a 2-parameter class of such spacetimes, and so the existence of a circular photon orbit is a highly specialised feature of a McVittie spacetime. However, we prove that in two large classes of McVittie spacetimes, there are bound particle and photon orbits: future-complete non-radial timelike and null geodesics along which the areal radius $r$ has a finite upper bound. These geodesics are asymptotic at large times to circular orbits of a corresponding Schwarzschild or Schwarzschild-de Sitter spacetime. The existence of these geodesics lays the foundations for and shows the theoretical possibility of the formation of accretion disks in McVittie spacetimes. We also summarize and extend some previous results on the global structure of McVittie spacetimes. The results on bound orbits are established using centre manifold and other techniques from the theory of dynamical systems.Comment: 26 pages, 12 figure

A regular C^0 singularity is not necessarily weak

Examples of space-times are given which contain scalar curvature singularities whereat the metric tensor is regular and continuous, but which are gravitationally strong. Thus the argument that such singularities are necessarily weak is incomplete; in particular the question of the gravitational strength of the null Cauchy horizon singularity which occurs in gravitational collapse remains open

Sectors of spherical homothetic collapse

A study is undertaken of the gravitational collapse of spherically symmetric thick shells admitting a homothetic Killing vector field under the assumption that the energy momentum tensor corresponds to the absence of a pure outgoing component of field. The energy-momentum tensor is not specified beyond this, but is assumed to satisfy the strong and dominant energy conditions. The metric tensor depends on only one function of the similarity variable and the energy conditions identify a class of functions ${\cal F}$ to which the metric function may belong. The possible global structure of such space-times is determined, with particular attention being paid to singularities and their temporal nature (naked or censored). It is shown that there are open subsets of ${\cal F}$ which correspond to naked singularities; in this sense, such singularities are stable. Furthermore, it is shown that these singularities can arise from regular (continuous), asymptotically flat initial data which deviate from the trivial data by an arbitrarily small amount.Comment: Now 40pp. plain latex including 11 of figures (using pstricks.tex). Some proofs omitted for brevity (these are available in V1). To appear in Classical and Quantum Gravit

Local properties and global structure of McVittie spacetimes with non-flat FLRW backgrounds

McVittie spacetimes embed the vacuum Schwarzschild(-(anti) de Sitter) spacetime in an isotropic FLRW background universe. We study the global structure of McVittie spacetimes with spatially non-flat FLRW backgrounds. This requires the extension of the definition of such spacetimes, previously given only for the flat and open cases, to the closed case. We revisit this definition and show how it gives rise to a unique spacetime (given the FLRW background, the mass parameter $M$ and the cosmological constant $\Lambda$) in the open and flat cases. In the closed case, an additional free function of the cosmic time arises. We derive some basic results on the metric, curvature and matter content of McVittie spacetimes and derive a representation of the line element that makes the study of their global properties possible. In the closed case (independently of the free function mentioned above), the spacetime is confined (at each instant of time) to a region bounded by a minimum and a maximum area radius, and is bounded either to the future or to the past by a scalar curvature singularity. This allowed region only exists when the background scale factor is above a certain minimum. In the open case, radial null geodesics originate in finite affine time in the past at a boundary formed by the union of the Big Bang singularity of the FLRW background and a non-singular hypersurface of varying causal character. Furthermore, in the case of eternally expanding open universes, we show that black holes are ubiquitous: ingoing radial null geodesics extend in finite affine time to a hypersurface that forms the boundary of the region from which photons can escape to future null infinity. We revisit the black hole interpretation of McVittie spacetimes in the spatially flat case, and show that this interpretation holds also in the case of a vanishing cosmological constant, contrary to a previous claim of ours.Comment: 46 + 4 pages, 7 figure

A geodesically complete space-time with a crushing null hypersurface

Withdrawn; conclusion that the singularity is strong is incorrect.Comment: 4 pages, Revte

Geometry and topology of singularities in spherical dust collapse

We derive some more results on the nature of the singularities arising in the collapse of inhomogeneous dust spheres. (i) It is shown that there are future-pointing radial and non-radial time-like geodesics emerging from the singularity if and only if there are future-pointing radial null geodesics emerging from the singularity. (ii) Limits of various space-time invariants and other useful quantities (relating to Thorne's point-cigar-barrel-pancake classification and to isotropy/entropy measures) are studied in the approach to the singularity. (iii) The topology of the singularity is studied from the point of view of ideal boundary structure. In each case, the different nature of the visible and censored region of the singularity is emphasized.Comment: 12 pages. To appear in Classical and Quantum Gravit

On global models for finite rotating objects in equilibrium in cosmological backgrounds

The studies in general relativity of rotating finite objects in equilibrium have usually focused on the case when they are truly isolated, this is, the models to describe finite objects are embedded in an asymptotically flat exterior vacuum. Known results ensure the uniqueness of the vacuum exterior field by using the boundary data for the exterior field given at the surface of the object plus the decay of the exterior field at infinity. The final aim of the present work is to study the consequences on the interior models by changing the boundary condition at infinity to one accounting for the embedding of the object in a cosmological background. Considering first the FLRW standard cosmological backgrounds, we are studying the general matching of FLRW with stationary axisymmetric spacetimes in order to find the new boundary condition for the vacuum region. Here we present the first results.Comment: LaTeX, 6 pages, uses ere04.cls style, to appear in the proceedings of the Spanish Relativity Meeting ERE'0