Physics
Scientific paper
Aug 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977gregr...8..631h&link_type=abstract
General Relativity and Gravitation, vol. 8, Aug. 1977, p. 631-645.
Physics
48
Cosmology, Field Theory (Physics), Gravitation Theory, Relativity, Conservation Laws, Gravitational Constant, Green'S Functions, Laplace Equation, Newton Theory
Scientific paper
Three alternative general relativistic theories of gravitation with fourth-order field equations are evaluated which were suggested by Weyl (1919) and Eddington (1924). It is shown that in the presence of extended sources, none of these alternatives leads to Newton's law of gravitation in the nonrelativistic limit. An analysis is performed which indicates that if only asymptotic agreement with Newton's law is required, the Einstein tensor can be supplemented by the introduction of terms involving higher-order derivatives of the metric and universal constants having the dimension of length. It is concluded that: (1) the special theory of relativity can be fitted into an infinity of general relativistic theories, (2) only Einstein's general theory yields an acceptable theory of gravitation without the introduction of additional universal constants, and (3) Birkhoff's (1923) theorem on the existence of a unique one-parameter family of spherically symmetric solutions to the vacuum field equations does not hold for any of the examined generalizations of Einstein's equations.
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