Second order gravitational field theories with Hilbert gauge

Physics

Scientific paper

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Field Theory (Physics), Gauge Invariance, Gravitation Theory, Hilbert Transformation, Relativity, Space-Time Functions, Equations Of Motion, Tensors

Scientific paper

A field theoretical approach to a class of gravitational theories, deducible by a variational principle is considered in pseudo-Euclidean space-time. The first order of the theory assumes to measure space and time by ideal rods and clocks unaffected by gravity, but constituted of matter obeying all the other laws of physics, and satisfying the requirements of Einstein's special relativity. By coupling the gravitational potential with the total energy-momentum tensor instead of with the particle tensor, the second order field equations are derived. The Hilbert gauge is assumed to assure the exclusion of the vector component of the gravitational potential. The second order equations of motion are derived from the field equations assuming a variational principle and using a new interaction Langrangian density. Available results of experiments are compared to the predictions of the theories.

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