2014/01/31 by Eolo Di Casola, Stefano Liberati, Sebastiano Sonego
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmological constant #Cosmology and Gravitation Theories #Equivalence principle (geometric) #General relativity #Geodesic #Gravitation #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Noncommutative and Quantum Gravity Theories #Physics #Quantum mechanics #Spacetime #Theoretical physics #gr-qc
paper · pdf · doi:10.1103/physrevd.89.084053
published as Physical Review D 89, 084053 (2014) · 17 pages, no figures. Tiny modifications to match the published version
openalex publication_date 2014/04/10 · arxiv created 2014/04/11 · arxiv updated 2014/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 (as well as with a cosmological constant term) and scalar-tensor theories, but extends also to debated or unknown scenarios, such as the 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.