The occurrence of singularities in cosmology

  title={The occurrence of singularities in cosmology},
  author={Stephen William Hawking},
  journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences},
  pages={511 - 521}
  • S. Hawking
  • Published 20 December 1966
  • Physics, Mathematics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
It is shown that singularities of space-time are inevitable if the Einstein equations hold, if matter has normal properties and if the universe satisfies certain reasonable global conditions. The singularities would be in the past and would, in principle, be observable. Observation to determine whether such singularities actually occurred would provide a powerful test of the Einstein equations in strong fields. The singularity would not necessarily constitute a beginning of the universe. 

The singularities of gravitational collapse and cosmology

  • S. HawkingR. Penrose
  • Mathematics
    Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected if

Numerical Approaches to Spacetime Singularities

  • B. Berger
  • Physics
    Living reviews in relativity
  • 2002
Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.

Einstein equation at singularities

Einstein’s equation is rewritten in an equivalent form, which remains valid at the singularities in some major cases. These cases include the Schwarzschild singularity, the

Through the Big Bang in inflationary cosmology

  • F. Mercati
  • Mathematics
    Journal of Cosmology and Astroparticle Physics
  • 2019
Singularities in General Relativity are regions where the description of spacetime in terms of a pseudo-Riemannian geometry breaks down. The theory seems unable to predict the evolution of the

On singularity theorems and curvature growth

It is shown that the proofs of a series of classical singularity theorems of general relativity can be modified such that these theorems also state the maximality of the incomplete nonspacelike

A semiclassical singularity theorem

Quantum fields do not satisfy the pointwise energy conditions that are assumed in the original singularity theorems of Penrose and Hawking. Accordingly, semiclassical quantum gravity lies outside

Some cosmological models with spin and torsion, I

The Einstein-Cartan theory, which is a slight modification of the general theory of relativity, is almost indistinguishable in its practical consequences from the latter theory. A characteristic

Black holes in Einstein-Maxwell Theory

We prove variants of known singularity theorems ensuring the existence of a region of finite lifetime that are particularly well applicable if the solution admits a conformal extension, a property

A singularity theorem for evaporating black holes

The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. Here, we provide motivation for an energy condition obeyed in

A gravitational collapse singularity theorem consistent with black hole evaporation

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the



Geometry of Manifolds

Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second

geometry of manifolds. A cadem ic P ress. C arte r

  • B . 1966 Phys. Rev
  • 1964