Generally Covariant Integral Formulation of Einstein's Field Equations

1969/11/25 by D. W. Sciama, P. C. Waylen, Robert C. Gilman · 1 voice · 8 citations
Computer Science · Engineering · Physics and Astronomy · #Computational Physics and Python Applications #Experimental and Theoretical Physics Studies #Geophysics and Sensor Technology

paper · doi:10.1103/physrev.187.1762

openalex publication_date 1969/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11

Abstract

As a basis for a generally covariant theory of Mach's principle, we express Einstein's field equations in integral form. The nonlinearity of these equations is reflected in the kernel of the integral representation, which is a functional of the metric tensor. The functional dependence is so constructed that, subject to supplementary conditions, the kernel may be regarded as remaining unchanged to the first order when a small change in the source produces a corresponding change in the potential. To obtain this kernel, a linear differential operator is derived by varying a particular form of Einstein's field equations. The elementary solution corresponding to this linear operator provides the kernel of an approximate integral representation which becomes exact in the limit of vanishing variations. This representation is in a certain sense unique. Our discussion is confined to a normal neighborhood of the field point.

Citations

• On the Origin of Inertia

Cited by

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• A new family of gauges in linearized general relativity
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Discussions

• Sciama's 1953 paper was not a fringe work and is still reasonably well-known - Google Scholar reports ~300 citations in the last ten years – but its importance was not as an experimentally testable th [stackexchange, 4 points]

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