Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2000-11-25
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
17 pages, LATEX 2e
Scientific paper
Singularity theorems of general relativity utilize the notion of causal geodesic incompleteness as a criterion of the presence of a spacetime singularity. The incompleteness of a causal curve implies the end and/or beginning of the existence of a particle, which is an event. In the commonly accepted approach, singularities are not incorporated into spacetime. Thus spacetime turns out to be event-incomplete. With creation from nothing, singularities are sources of lawlessness. A straightforward way around those conceptual problems consists in including metric singularities in spacetime and then matching metrics and causal geodesics at the singularities. To this end, a spacetime manifold is assumed to be unboundable, so that singularities may only be interior. The matching the geodesics is achieved through weakening conditions for their smoothness. This approach is applied to a black-white hole and a big crunch-bang.
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