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arXiv · 1206.5341

Two Theorems on Flat Space-Time Gravitational Theories

Mario Castagnino·Luis Chimento
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Abstract

The first theorem states that all flat space-time gravitational theories must have a Lagrangian with a first term that is an homogeneous (degree-I) function of the 4-velocity $u^i$, plus a functional of $η_{ij}u^i u^j$. The second theorem states that all gravitational theories that satisfy the strong equivalence principle have a Lagrangian with a first term $g_{ij}(x)u^i u^j$ plus an irrelevant term. In both cases the theories must issue from a unique variational principle. Therefore, under this condition it is impossible to find a flat space-time theory that satisfies the strong equivalence principle.

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Mario Castagnino, Luis Chimento. 2012-06-23. Two Theorems on Flat Space-Time Gravitational Theories. https://doi.org/10.1007/bf00763058

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