Toward a field theory of gravitation
A new theory of gravitation is presented in which the righ-hand side of the field equations contains the gravitational-field stress-energy tensortμν. The crucial new information leading to this construction is the demonstration that the two basic differential identities of space-time geometry (that of Bianchi and that of Freud) require atrue gravitational field stress-energy tensortμν which must be added to the matter tensor τμν. Otherwise, the two identities clash and lead to a mathematical overdetermination which creates insurmountable internal difficulties for the curved-space-time theory of gravitation as a whole.
KeywordsPACS 04.20.Cv Fundamental problems and general formalism PACS 04.60 Quantum theory of gravitation PACS 95.10.Ce Celestial mechanics
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