A new geometrical gravitational theory.

Details A new geometrical gravitational theory. A new geometrical gravitational theory.

Apr 1981

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1981gregr..13..313o&link_type=abstract

General Relativity and Gravitation, Volume 13, Issue 4, pp.313-334

Mathematics

Logic

5

Gravitation Theory

Scientific paper

A geometrical gravitational theory based on the connection Γ{/βγ α }={{/βγ α }} + δ{β/α}∂γ lnϕ + δ{γ/α}∂β lnϕ -g βγ∂α ln ψ is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter Ω2. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg μν and two gauge scalarsϕ andψ. Physically the gravitational potential corresponds tog μν in the same way as in general relativity, the gravitational coupling constant toψ -2, and the gravitational mass tou(ϕ, ψ), which is a coscalar of power -1 algebraically made ofϕ andψ. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(ϕ, ψ)=ϕ on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power -4 algebraically made ofψ andu(ϕ, ψ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter Ω2 is experimentally determined by applying the solutions to the solar system.

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