The Arnowitt–Deser–Misner (ADM) equations are deeply in-tertwined 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.
The role of elliptic operators in the initial-value problem for general relativity / Esposito, G; Stornaiolo, C. - (2002), pp. 130-138. (Intervento presentato al convegno General Relativity, Cosmology and Gravittational Lensing tenutosi a Vietri Sul Mare nel December 2000).
The role of elliptic operators in the initial-value problem for general relativity
ESPOSITO GPrimo
;
2002
Abstract
The Arnowitt–Deser–Misner (ADM) equations are deeply in-tertwined 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.| File | Dimensione | Formato | |
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