The Role of Elliptic Operators in the Initial-Value Problem for General Relativity
General Relativity and Quantum Cosmology
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.gr-qc/0012064,
title = {The Role of Elliptic Operators in the Initial-Value Problem for General Relativity},
author = {Giampiero Esposito and Cosimo Stornaiolo},
journal= {arXiv preprint arXiv:gr-qc/0012064},
year = {2007}
}
Comments
9 pages, Latex