Tensor Theory Of Gravitation Research Articles

A tensor theory of gravitation in a curved metric on a flat background

A theory of gravity is proposed using a tensor potential for the field on a flat metric. This potential cannot be isolated by local observations, but some details can be deduced from measurement at a distance. The requirement that the field equations for the tensor potential shall be deducible from an action integral, that the action and field equations are gauge invariant, and, conversely, that the Lagrangian in the action integral can be integrated from the field equations leads to Einstein's field equations. The requirement that the field energy-momentum tensor exists leads to a constraint on the tensor potential. If the constraint is a differential gauge condition, then it can only be the Hilbert condition giving a unique background tensor, metric tensor and tensor potential. For a continuous field inside a solid sphere the metric must be homogeneous in the spatial coordinates, and the associated field energy-momentum tensor has properties consistent with Newtonian dynamics.

Mach's principle and a new gauge freedom in Brans-Dicke theory

The relationship between Mach's principle and the Brans-Dicke scalar- tensor theory of gravitation is discussed. A converse formulation is proposed. It is shown that the geometry of space-time determines the mass- energy content only up to a position dependent gauge transformation. This is interpreted as a scale change in the unit of mass which preserves the conservation laws. For arbitrary values of the scalar field coupling constant omega the theory is invariant only under a restricted group of gauge transformations. Complete invariance applies in the case omega =0. Furthermore it is shown that whenever the curvature scalar R vanishes the theory can be transformed into the usual form of Einstein's general relativity. Equivalence classes of solutions are defined which have the same geometry and lead to the same geodesic motion for test particles. Examples are constructed for the case of static spherical symmetry and for uniform cosmology which exhibit these properties. Some further consequences are discussed.