Foundations of Physics 29 (12):1977-1985 (1999)

Abstract
In a framework describing manifestly covariant relativistic evolution using a scalar time τ, consistency demands that τ-dependent fields be used. In recent work by the authors, general features of a classical parametrized theory of gravitation, paralleling general relativity where possible, were outlined. The existence of a preferred “time” coordinate τ changes the theory significantly. In particular, the Hamiltonian constraint for τ is removed From the Euler-Lagrange equations. Instead of the 5-dimensional stress-energy tensor, a tensor comprised of 4-momentum density mid flux density only serves as the source. Building on that foundation, in this paper we develop a linear approximate theory of parametrized gravitation in the spirit of the flat spacetime approach to general relativity. Using a modified form of Kraichnan's flat spacetime derivation of general relativity, we extend the linear theory to a family of nonlinear theories in which the flat metric and the gravitational field coalesce into a single effective curved metric
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DOI 10.1023/A:1018802719705
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References found in this work BETA

On Parametrized General Relativity.J. Brian Pitts & W. C. Schieve - 1998 - Foundations of Physics 28 (9):1417-1424.

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Flat Spacetime Gravitation with a Preferred Foliation.J. B. Pitts & W. C. Schieve - 2001 - Foundations of Physics 31 (7):1083-1104.

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