98 research outputs found
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
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 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.
and pointwise bounds are also obtained for the multipoles of a minimally
coupled massive scalar wave packet.Comment: 16 pages, 1 figure. Published versio
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 . 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
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 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
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
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 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
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
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 and the cosmological constant ) 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
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
Geometric properties of a 2-D space-time arising in 4-D black hole physics
The Schwarzschild exterior space-time is conformally related to a direct
product space-time, , where is a
two-dimensional space-time. This direct product structure arises naturally when
considering the wave equation on the Schwarzschild background. Motivated by
this, we establish some geometrical results relating to that
are useful for black hole physics. We prove that has the rare
property of being a causal domain. Consequently, Synge's world function and the
Hadamard form for the Green function on this space-time are well-defined
globally. We calculate the world function and the van Vleck determinant on
numerically and point out how these results will be used to
establish global properties of Green functions on the Schwarzschild black hole
space-time.Comment: 19 pages, 6 figure
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