Homothetic and conformal motions in spacelike slices of solutions of Einstein's equations

Journal Article · Thu Jul 01 04:00:00 EDT 1976 · J. Math. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1063/1.523052· OSTI ID:7364050

Berger, B K

Components of Killing's equation are used to obtain constraints satisfied in a spacelike hypersurface by the intrinsic metric and extrinsic curvature in the presence of a spacetime conformal motion for a solution of Einstein's equations. If the conformal motion is either a homothetic motion or a motion, it is shown that these Killing constraints are preserved by the Einstein evolution equations. It is then shown that the generator of the homothetic motion (homothetic Killing vector) can be constructed if the Killing constraints are satisfied by a set of initial data. It is shown that a homothetic motion in the intrinsic metric is a spacetime homothetic motion if the extrinsic curvature is transformed correctly under the spatial homothetic motion. Further restrictions on a proper conformal motion due to the fact that it is not identically a curvature collineation are obtained. Restrictions on the matter--stress--energy tensor are discussed. Examples are presented. (AIP)

• Research Organization: Physics Department, Yale University, New Haven, Connecticut 06520
• OSTI ID: 7364050
• Journal Information: J. Math. Phys. (N.Y.); (United States), Journal Name: J. Math. Phys. (N.Y.); (United States) Vol. 17:7; ISSN JMAPA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
EINSTEIN FIELD EQUATIONS
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
GENERAL RELATIVITY THEORY
METRICS
SPACE-TIME
TENSORS
TRAJECTORIES