arXiv subjects

Susan M. Scott

Publications and source records attributed to Susan M. Scott.

22 records · Page 2Linked to original sources

arXiv2001

Isotropic singularities in shear-free perfect fluid cosmologies

We investigate barotropic perfect fluid cosmologies which admit an isotropic singularity. From the General Vorticity Result of Scott, it is known that these cosmologies must be irrotational. In this paper we prove, using two different methods, that if we make the additional assumption that the perfect fluid is shear-free, then the fluid flow must be geodesic. This then implies that the only shear-free, barotropic, perfect fluid cosmologies which admit an isotropic singularity are the FRW models.

gr-qc↗

arXiv1998

Cosmological models with isotropic singularities

In 1985 Goode and Wainwright devised the concept of an isotropic singularity. Since that time, numerous authors have explored the interesting consequences, in mathematical cosmology, of assuming the existence of this type of singularity. In this paper, we collate all examples of cosmological models which are known to admit an isotropic singularity, and make a number of observations regarding their general characteristics.

gr-qc↗

arXiv1994

Invariance properties of boundary sets of open embeddings of manifolds and their application to the abstract boundary

The {\em abstract boundary\/} (or {\em {\em a\/}-boundary\/}) of Scott and Szekeres \cite{Scott94} constitutes a ``boundary'' to any $n$-dimensional, paracompact, connected, Hausdorff, $C^\infty$-manifold (without a boundary in the usual sense). In general relativity one deals with a {\em space-% time\/} $(\cM,g)$ (a 4-dimensional manifold $\cM$ with a Lorentzian metric $g$), together with a chosen preferred class of curves in $\cM$. In this case the {\em a\/}-boundary points may represent ``singularities'' or ``points at infinity''. Since the {\em a\/}-boundary itself, however, does not depend on the existence of further structure on the manifold such as a Lorentzian metric or connection, it is possible for it to be used in many contexts. In this paper we develop some purely topological properties of abstract boundary sets and abstract boundary points ({\em a\/}-boundary points). We prove, amongst other things, that compactness is invariant under boundary set equivalence, and introduce another invariant concept ({\em isolation\/}), which encapsulates the notion that a boundary set is ``separated'' from other boundary points of the same embedding. ....... [The abstract continues in paper proper - truncated to fit here.]

gr-qc↗

arXiv1994

The abstract boundary---a new approach to singularities of manifolds

A new scheme is proposed for dealing with the problem of singularities in General Relativity. The proposal is, however, much more general than this. It can be used to deal with manifolds of any dimension which are endowed with nothing more than an affine connection, and requires a family \calc\ of curves satisfying a {\em bounded parameter property} to be specified at the outset. All affinely parametrised geodesics are usually included in this family, but different choices of family \calc\ will in general lead to different singularity structures. Our key notion is the {\em abstract boundary\/} or {\em $a$-boundary\/} of a manifold, which is defined for any manifold \calm\ and is independent of both the affine connection and the chosen family \calc\ of curves. The $a$-boundary is made up of equivalence classes of boundary points of \calm\ in all possible open embeddings. It is shown that for a pseudo-Riemannian manifold $(\calm,g)$ with a specified family \calc\ of curves, the abstract boundary points can then be split up into four main categories---regular, points at infinity, unapproachable points and singularities. Precise definitions are also provided for the notions of a {\em removable singularity} and a {\em directional singularity}. The pseudo-Riemannian manifold will be said to be singularity-free if its abstract boundary contains no singularities. The scheme passes a number of tests required of any theory of singularities. For instance, it is shown that all compact manifolds are singularity-free, irrespective of the metric and chosen family \calc.

gr-qc↗