The Role of Elliptic Operators in the Initial-Value Problem for General Relativity

Details The Role of Elliptic Operators in the Initial-Value Problem for General Relativity The Role of Elliptic Operators in the Initial-Value Problem for General Relativity

2000-12-18

arxiv.org/abs/gr-qc/0012064v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

9 pages, Latex

Scientific paper

The Arnowitt-Deser-Misner (ADM) equations are deeply intertwined with discrete spectral resolutions of an elliptic operator of Laplace type associated with the spacelike hypersurfaces which foliate the space-time manifold, and the non-linearities of the four-dimensional hyperbolic theory are mapped into the potential term occurring in this operator. The ADM equations are here re-expressed as a coupled first-order system for the induced metric and the trace-free part of the extrinsic-curvature tensor, and their formulation in terms of integral equations is studied.

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