# On the structure of conformal singularities in classical general relativity

@article{Newman1993OnTS, title={On the structure of conformal singularities in classical general relativity}, author={Richard P.A.C. Newman}, journal={Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences}, year={1993}, volume={443}, pages={473 - 492} }

Consideration is given to Big Bang singularities which can be conformally transformed to a spacelike hypersurface, with the conformal factor and conformal metric both smooth on the extended manifold. A precise definition of such ‘conformal singularities’ is proposed by analogy with the established definition of conformal infinity. The energy tensor of the physical space-time is assumed to have a form appropriate to an isentropic perfect fluid. The smoothness condition implies that the adiabatic…

## 44 Citations

On the structure of conformal singularities in classical general relativity. II Evolution equations and a conjecture of K. P. Tod

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- 1993

Consideration is given to the Cauchy problem for perfect fluid space-times which evolve from an initial singularity of conformal type. The evolution equations for the conformally transformed,…

Geometric asymptotics and beyond

- Mathematics
- 2014

The analysis of Einstein's field equations in the context of Penrose's notion of asymptotic simplicity, which was originally intro- duced to provide a geometric setting for the investigation of…

On the nature of Hawking’s incompleteness for the Einstein-vacuum equations: The regime of moderately spatially anisotropic initial data

- MathematicsJournal of the European Mathematical Society
- 2021

In the mathematical physics literature, there are heuristic arguments, going back three decades, suggesting that for an open set of initially smooth solutions to the Einstein-vacuum equations in high…

Topological Early Universe Cosmology

- Mathematics
- 2021

The early history of the universe might be described by a topological phase followed by a standard second phase of Einstein gravity. To study this scenario in its full generality, we consider a…

Conformal Methods in General Relativity with application to Conformal Cyclic Cosmology: A minicourse given at the IXth IMLG Warsaw 2018

- Mathematics
- 2021

In these lectures my aim is to review enough of conformal differential geometry in four dimensions to give an account of Penrose’s conformal cyclic cosmology. 1 Tensor calculus and conformal…

2 EVOLUTION EQUATIONS AND CONSTRAINTS 2

- Mathematics

In this paper we investigate asymptotic isotropization. We derive the asymptotic dynamics of spatially inhomogeneous cosmological models with a perfect fluid matter source and a positive cosmological…

A conformal extension theorem based on null conformal geodesics

- Mathematics
- 2009

In this article we describe the formulation of null geodesics as null conformal geodesics and their description in the tractor formalism. A conformal extension theorem through an isotropic…

Theorems on Existence and Global Dynamics for the Einstein Equations

- MathematicsLiving reviews in relativity
- 2005

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations and some miscellaneous topics connected with the main theme are collected in a separate section.

6 Isotropic Cosmological Singularities

- Mathematics, Physics
- 2002

An isotropic cosmological singularity is a cosmological singularity which can be removed by conformally-rescaling the metric. In the rescaled metric, the singularity is required to occur on a…

Fuchsian analysis of S2 × S1 and S3 Gowdy spacetimes

- Mathematics
- 2001

The Gowdy spacetimes are vacuum solutions of the Einstein equations with two commuting Killing vectors having compact spacelike orbits with T3, S2 × S1 or S3 topology. In the case of T3 topology,…

## References

SHOWING 1-10 OF 31 REFERENCES

On the structure of conformal singularities in classical general relativity. II Evolution equations and a conjecture of K. P. Tod

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
- 1993

Consideration is given to the Cauchy problem for perfect fluid space-times which evolve from an initial singularity of conformal type. The evolution equations for the conformally transformed,…

Isotropic singularities in cosmological models

- Mathematics, Physics
- 1985

Motivated by the ideas of quiescent cosmology and Penrose's Weyl tensor hypothesis concerning the 'big bang', the authors give a geometric (and hence coordinate-independent) definition of the concept…

Zero rest-mass fields including gravitation: asymptotic behaviour

- Mathematics, PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1965

A zero rest-mass field of arbitrary spin s determines, at each event in space-time, a set of 2s principal null directions which are related to the radiative behaviour of the field. These directions…

Investigations in relativistic cosmology

- Physics
- 1963

Abstract (by translator) A detailed report is given here of the general investigations carried out by the authors in the field of relativistic cosmology during the past years. The paper consists of…

The Large Scale Structure of Space-Time

- Physics
- 1973

The theory of the causal structure of a general space-time is developed, and is used to study black holes and to prove a number of theorems establishing the inevitability of singualarities under certain conditions.

Velocity‐Dominated Singularities in Irrotational Dust Cosmologies

- Mathematics
- 1972

We consider irrotational dust solutions of the Einstein equations. We define ``velocity‐dominated'' singularities of these solutions. We show that a velocity‐dominated singularity can be considered…

Velocity‐Dominated Singularities in Irrotational Hydrodynamic Cosmological Models

- Mathematics
- 1972

We consider irrotational perfect fluid solutions of the Einstein equations with an equation of state p = γρ. We define ``velocity‐dominated'' singularities of these solutions, a notion previously…

A General Solution of the Einstein Equations with a Time Singularity

- Mathematics, Physics
- 1982

Abstract This paper is a concluding review exposition of the investigations aimed at the construction of a general cosmological solution of the Einstein equations with a singularity in time; thus it…

General Relativity; an Einstein Centenary Survey

- Physics
- 1979

List of contributors Preface 1. An introductory survey S. W. Hawking and W. Israel 2. The confrontation between gravitation theory and experiment C. M. Will 3. Gravitational-radiation experiments D.…

Dissipative effects in the expansion of the universe. I, II.

- Physics
- 1972

Consideration of dissipative processes in anisotropic homogeneous world models, showing that dissipation reduces the anisotropy. The viscosity approximation and its range of applicability is…