This paper examines the initial data for the evolution of the space–time solution of Einstein’s equations admitting a conformal symmetry. Under certain conditions on the extrinsic curvature of the initial complete spacelike hypersurface and sectional curvature of the space–time with respect to sections containing the normal vector field, we have shown that the initial hypersurface is conformally diffeomorphic to a sphere or a flat space or a hyperbolic space or the product of an open real interval and a complete 2-manifold. It has been further shown that if the initial hypersurface is compact, then it is conformally diffeomorphic to a sphere. Finally, the conformal symmetries of a generalized Robertson–Walker space–time have been described.
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April 2005
Research Article|
March 17 2005
Conformal symmetries of Einstein’s field equations and initial data
Ramesh Sharma
Ramesh Sharma
a)
Department of Mathematics, University of New Haven
, West Haven, Connecticut 06516
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Electronic mail: [email protected]
J. Math. Phys. 46, 042502 (2005)
Article history
Received:
November 30 2004
Accepted:
January 19 2005
Citation
Ramesh Sharma; Conformal symmetries of Einstein’s field equations and initial data. J. Math. Phys. 1 April 2005; 46 (4): 042502. https://doi.org/10.1063/1.1868372
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