arXiv subjects

Susan M Scott

Publications and source records attributed to Susan M Scott.

8 recordsLinked to original sources

arXiv2026

The relationship between spacetime singularities and regions at infinity

Ideal attached points are a core concept in general relativity for pseudo-Riemannian manifolds, and whether the spacetime can be extended with certain properties is a central consideration in their choice. This paper establishes a sufficient condition for the separability between singularities and points at infinity for any maximally extended pseudo-Riemannian manifold. We focus on the incomplete geodesics of $(\mathcal{M},g)$, and produce an envelopment $(\mathcal{M},g,\hat{\mathcal{M}})$ of the spacetime such that an incomplete geodesic $\gamma:[0,1) \rightarrow \mathcal{M}$ has an endpoint $q$ in $\hat{\mathcal{M}}$. If there is no pair of geodesics approaching $q$ which is intertwined, then $q$ is a singularity. Additionally, $q$ will not be approached by any geodesic with infinite affine parameter, and therefore cannot cover a point at infinity, thereby rendering it a {\it pure singularity} in the abstract boundary framework. We apply the Endpoint Theorem to the maximal g-boundary introduced by Graf and Beld-Serrano in arXiv:2307.11034, and also provide a result on the separability between directional singularities and pure singularities. This analysis is then applied to the Schwarzschild spacetime.

gr-qc↗

arXiv2021

The Endpoint Theorem

The Endpoint Theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It plays a fundamental role in the theory of the Abstract Boundary as it implies that there is always an Abstract Boundary boundary point to represent the endpoint of such sequences and curves. The Endpoint Theorem will be of interest to researchers analysing specific spacetimes as it shows how to construct a chart in the original manifold which contains the sequence (curve). In particular, it has application to the study of singularities predicted by the singularity theorems.

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arXiv2010

Conformal formulation of cosmological futures

We summarise the new conformal framework of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity. Both new definitions are motivated by, but not restricted to quiescent cosmology and the Weyl curvature hypothesis, which previously only possessed a framework for a classical initial state of the universe, namely the Isotropic Singularity. Some of the features of the framework are briefly discussed.

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arXiv2010

Encoding cosmological futures with conformal structures

Quiescent cosmology and the Weyl curvature hypothesis possess a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary to also encode appropriate cosmological futures. In order to devise a new framework we analyse the relation between regular conformal structures and (an)isotropy, the behaviour and role of a monotonic conformal factor which is a function of cosmic time, as well as four example cosmologies for further guidance. Finally, we present our new definitions of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity which offer a promising realisation for the new framework. Their irregular, degenerate conformal structures differ significantly from those of the Isotropic Singularity. The combination of the three definitions together could then provide the first complete formalisation of the quiescent cosmology concept. For completeness we also present the new definitions of an Isotropic Future Singularity and a Future Isotropic Universe. The relation to other approaches, in particular to the somewhat dual dynamical systems approach, and other asymptotic scenarios is briefly discussed.

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arXiv2010

Quiescent cosmology and the final state of the universe

It has long been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A school of thought for its explanation is quiescent cosmology, which already possesses a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary in order to also describe possible final states of the universe. Our new definitions of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity, whose structure and properties differ significantly from those of the Isotropic Singularity, offer a promising realisation for this framework. The combination of the three definitions together may then provide the first complete formalisation of the quiescent cosmology concept.

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arXiv2004

The ACIGA Data Analysis programme

The Data Analysis programme of the Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) was set up in 1998 by the first author to complement the then existing ACIGA programmes working on suspension systems, lasers and optics, and detector configurations. The ACIGA Data Analysis programme continues to contribute significantly in the field; we present an overview of our activities.

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arXiv2002

Network sensitivity to geographical configuration

Gravitational wave astronomy will require the coordinated analysis of data from the global network of gravitational wave observatories. Questions of how to optimally configure the global network arise in this context. We have elsewhere proposed a formalism which is employed here to compare different configurations of the network, using both the coincident network analysis method and the coherent network analysis method. We have constructed a network model to compute a figure-of-merit based on the detection rate for a population of standard-candle binary inspirals. We find that this measure of network quality is very sensitive to the geographic location of component detectors under a coincident network analysis, but comparatively insensitive under a coherent network analysis.

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arXiv2001

GRworkbench: A Computational System Based on Differential Geometry

We have developed a new tool for numerical work in General Relativity: GRworkbench. While past tools have been ad hoc, GRworkbench closely follows the framework of Differential Geometry to provide a robust and general way of computing on analytically defined space-times. We discuss the relationship between Differential Geometry and C++ classes in GRworkbench, and demonstrate their utility.

gr-qc↗