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}
}
  • R. Newman
  • Published 8 December 1993
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
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… 
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    Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
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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
  • R. Newman
  • Mathematics
    Proceedings 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
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
  • R. Penrose
  • Mathematics, Physics
    Proceedings 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
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
TLDR
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
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Velocity‐Dominated Singularities in Irrotational Hydrodynamic Cosmological Models
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A General Solution of the Einstein Equations with a Time Singularity
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
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.
Consideration of dissipative processes in anisotropic homogeneous world models, showing that dissipation reduces the anisotropy. The viscosity approximation and its range of applicability is
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