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Cauchy problem; problem of singularities; Penrose’s theorem; general relativity

Linearized solution of Datta in a non-symmetric and isentropic motion of a perfect fluid is studied by dealing with a Cauchy problem in co-moving coordinates in the framework of general relativity. The problem of singularities is discussed from the standpoint of a local observer both for rotating and non-rotating fluids. It is shown that, whatever the distribution of matter, a singularity which occurred in the past in both the rotating and non-rotating parts of the universe must occur again later after some finite proper time, if the universe is closed. A modification is incorporated in Penrose’s theorem by explicitly exhibiting that the universe defined by Penrose can possess a Cauchy hypersurface.

Bidyut Kumar Datta¹

1. S N Bose Institute of Physical Sciences, Calcutta University, Calcutta - 700 009

Published

September 1977

Manuscript received

8 April 1976

Manuscript revised

31 January 1977