Special conformal symmetries in general relativity

Details Special conformal symmetries in general relativity Special conformal symmetries in general relativity

Feb 1990

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990gregr..22..203h&link_type=abstract

General Relativity and Gravitation, Volume 22, Issue 2, pp.203-215

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12

Scientific paper

A geometrical discussion of special conformal vector fields in space-time is given. In particular, it is shown that if such a vector fieldξ is admitted, it is unique up to a constant scaling and the addition of a homothetic or a Killing vector field. In the case when the gradient of the conformal scalar associated withξ is non-null it is shown that other homothetic and affine symmetries are necessarily admitted by the space-time, that an intrinsic family of 2-dimensional flat submanifolds is determined in the space-time, thatξ is, in general, hypersurface orthogonal and that the space-time, if non-flat, is necessarily (geodesically) incomplete. Other geometrical features of such space-times are also considered.

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