Non-local equations for general relativity

The field equations for two non-local variables, equivalent to the Einstein vacuum equations, are presented. These variables are the holonomy operator associated with special paths and the light cone cut function. Starting from these equations, one shows via a perturbation argument that a single, fo...

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Bibliographic Details
Published in:Journal of geometry and physics 1992, Vol.8 (1), p.195-209
Main Authors: Kozameh, Carlos N., Newman, Ezra T., Iyer, Savitri V.
Format: Article
Language:English
Subjects:
general relativity
non-local equations
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Summary:The field equations for two non-local variables, equivalent to the Einstein vacuum equations, are presented. These variables are the holonomy operator associated with special paths and the light cone cut function. Starting from these equations, one shows via a perturbation argument that a single, fourth-order equation for the cut function can be derived. This single equation encodes the entire conformal structure of a vacuum space—time. The same perturbation technique yields, via quadratures, solutions to the vacuum Einstein equations to any order.
ISSN:0393-0440
1879-1662
DOI:10.1016/0393-0440(92)90048-6