Generalised Functions and Singularities of Einstein’s equations

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• James Vickers (Southampton, Maths)
• Thursday 23 March 2017, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

This talk will describe how singularities of Einstein’s equations are treated within the theory of General Relativity. In other field theories, such as electromagnetism, an important role is played by point charges, line sources and surface charges. Mathematically such concentrated sources are described using the classical theory of distributions. However Einstein’s equations are a system of non-linear PDEs so that one cannot use classical distribution theory. This talk will explain how a non-linear theory of generalised functions (Colombeau algebras) may be used to describe important physical solutions of Einstein’s equations such as Cosmic Strings, shells of matter and impulsive gravitational waves. It will also give a recent new description of gravitational singularities in terms of the evolution of test fields rather than the traditional definition using world lines of test particles. It will end by relating this work to new developments in the theory of PDEs.

This talk is part of the Theoretical Physics Seminars series.

This talk is included in these lists:

• Bham Talks
• Theoretical Physics Seminars
• Theory Library
• What's on in Physics?

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