Weak equivalence principle for self-gravitating bodies: A sieve for purely metric theories of gravity

Abstract

We propose the almost-geodesic motion of self-gravitating test bodies as a possible selection rule among metric theories of gravity. Starting from a heuristic statement, the "gravitational weak equivalence principle", we build a formal, operative test able to probe the validity of the principle for any metric theory of gravity, in an arbitrary number of spacetime dimensions. We show that, if the theory admits a well-posed variational formulation, this test singles out only the purely metric theories of gravity. This conclusion reproduces known results in the cases of general relativity (also with a cosmological constant term), and scalar-tensor theories, but extends also to debated or unknown scenarios, such as f(R) and Lanczos-Lovelock theories. We thus provide new tools going beyond the standard methods, where the latter turn out to be inconclusive or inapplicable.

17 pages, no figures. Tiny modifications to match the published version

References in corpus (6)

• The Confrontation between General Relativity and Experiment
• The modified Newtonian dynamics-MOND-and its implications for new physics
• Holography of Gravitational Action Functionals
• Theory of gravitation theories: a no-progress report
• Scalar Gravitation and Extra Dimensions
• The strong equivalence principle from gravitational gauge structure

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