Singularities - The state of the art

Details Singularities - The state of the art Singularities - The state of the art

Feb 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..129c&link_type=abstract

General Relativity and Gravitation, vol. 8, Feb. 1977, p. 129-137.

Mathematics

15

Relativity, Singularity (Mathematics), Space-Time Functions, Boundary Value Problems, Cauchy Problem, Existence Theorems, Geodesic Lines, Points (Mathematics)

Scientific paper

The main results on singularities in 'classical' general relativity that have been proven so far are presented in a unified setting and in as self-contained a form as possible without embarking on detailed proofs. 'Incompleteness theorems' are reviewed which concern the existence of geodesics that cannot be continued to arbitrarily large positive or negative values of their affine parameter, and it is shown how incompleteness theorems are connected with the occurrence of singularities as they are now understood. Consideration is given to boundary points in curved space-time, the nature of singularities is discussed in terms of singularity theorems, and the special cases of a primordial singularity and of singular 'holes' in space-time are examined. It is noted that the nature and existence of singularities become doubtful once the predictable region of a Cauchy development is transcended.

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