A Class of Metric Theories of Gravitation on Minkowski Spacetime

A. Nairz

Institut für Theoretische Physik der Universität Innsbruck,
A-6020 Innsbruck, Technikerstr. 25, Austria

Received April 26, 1995; revised January 22, 1996

Abstract. A class of metric theories of gravitation on Minkowski spacetime is considered, which is - provided that certain assumptions (staying close to the original ideas of Einstein) are made - the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric) is defined by means of a second-rank tensor field S (referred to as gravitational potential). The theory is defined by a Lagrangian tex2html_wrap_inline23 , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.

Foundations of Physics 26, 369-389 (1996).
Errata: Foundations of Physics 27, 823-826 (1997).

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