Inertia and Gravity: a New Approach to Dynamical Theory in General Relativity

A new approach to gravitational field dynamics is proposed, as an alternative to the standard formulation of General Relativity. The spacetime metric tensor is split, into an externally fixed background geometry (inertia) and a local dynamical field (gravity); and a dynamical theory of matter and gravity in the inertial background is developed. The physical origin of inertia (Mach's Principle), and its observable properties, are discussed. The coordinate representations of inertia and gravity are found to have an internal gauge degree of freedom, due to the Equivalence Principle; the transformation properties of these fields, and the notion of covariant gauge conditions, are discussed. The dynamics of matter and gravitic fields is then investigated, using: (i) The group of motion of the inertial background, appearing as an externally fixed Lie symmetry in the matter and gravity action principles, which yields weakly conserved energy‐momentum‐like objects; and (ii) an internal symmetry gauge group, yielding strongly conserved “internal currents”. A fully covariant field‐theoretical formalism is used, in which all quantities and operations are tensorial ; the well‐known difficulties of “coordinate effects” in the standard nontensorial formulation are thus avoided. The physical significance of various types of conservation laws is discussed; and a complete family of energy‐momentum tensors of gravity, covariantly conserved together with the matter energy‐momentum, is deduced from a tensorial action principle. Treating gravity as an independent dynamical interaction, on an equal footing with other (matter) interactions, we are then finally led to the conclusion that the gravitic energy‐momentum of a system is fully determined by the matter energy‐momentum; various physical implications of this are discussed in some detail.