The Quantum Structure of Space and Time (293 pages)

Session 3

Singularit ies

Chair: Gary T. Horowitz, UCSB, USA

Rapporteur: Gary W. Gibbons, DAMPT, Cambridge, UK

Scientific secretary: Jan. Troost (Ecole Normale Supkrieure, Paris, France)

3.1 Rapporteur talk: Singularities, by Gary W. Gibbons

3.1.1 Introduction

Einstein’s General Relativity is incomplete because

0 It predicts that gravitational collapse , both at the Big Bang and inside black

holes, brings about spacetime singularities as at which the theory breaks down

0 It gives no account of ‘matter ’as opposed to geometry , and in particular the

nature of classical ‘particles ’

0 It is incompatible with quantum mechanics

I have been asked to review the first problem.

I will cover the following topics.

0 Singularity Theorems

0 Cosmic Censorship

0 Classical Boundary conditions and stabiity

0 Higher dimensional resolutions

0 Singularities at the end of Hawking Evaporation

0 Maldacena’s conjecture

3.1.2 Singularity Theorems

First discovered in Friedmann-Lemaitre models, it was shown by Roger Penrose [19]

that these arise if closed trapped surfaces occur during gravitational collapse and

work by Geroch , Hawking and Penrose [20] showed that as long as matter satisfies

various positive energy conditions, then spacetime singularities are inevitable

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