A geodesically complete space-time with a crushing null hypersurface
Withdrawn; conclusion that the singularity is strong is incorrect.
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arXiv subjects
Brien C. Nolan
Publications and source records attributed to Brien C. Nolan.
Strengths of singularities in spherical symmetry
Covariant equations characterizing the strength of a singularity in spherical symmetry are derived and several models are investigated. The difference between central and non-central singularities is emphasised. A slight modification to the definition of singularity strength is suggested. The gravitational weakness of shell crossing singularities in collapsing spherical dust is proven for timelike geodesics, closing a gap in the proof.
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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.
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A point mass in an isotropic universe. Existence, uniqueness and basic properties
Criteria which a space-time must satisfy to represent a point mass embedded in an open Robertson--Walker (RW) universe are given. It is shown that McVittie's solution in the case $k=0$ satisfies these criteria, but does not in the case $k=-1$. Existence of a solution for the case $k=-1$ is proven and its representation in terms of an elliptic integral is given. The following properties of this and McVittie's $k=0$ solution are studied; uniqueness, behaviour at future null infinity, recovery of the RW and Schwarzschild limits, compliance with energy conditions and the occurence of singularities. Existence of solutions representing more general spherical objects embedded in a RW universe is also proven.
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Yang's gravitational theory
Yang's pure space equations (C.N. Yang, Phys. Rev. Lett. v.33, p.445 (1974)) generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.
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A Characterisation of Strong Wave Tails in Curved Space-Times
A characterisation of when wave tails are strong is proposed. The existence of a curvature induced tail (i.e. a Green's function term whose support includes the interior of the light-cone) is commonly understood to cause backscattering of the field governed by the relevant wave equation. Strong tails are characterised as those for which the purely radiative part of the field is backscattered. With this definition, it is shown that electromagnetic waves in asymptotically flat space-times and fields governed by tail-free propagation have weak tails, but minimally coupled scalar fields in a cosmological scenario have strong tails.
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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.
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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.
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