Mancini, Christian and Tino, Guglielmo Maria and Capozziello, Salvatore (2025) Equivalent Gravities and Equivalence Principle: Foundations and experimental implications. Foundations of Physics, 55 (69).

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Abstract

The so-called Geometric Trinity of Gravity includes General Relativity (GR), based on spacetime curvature; the Teleparallel Equivalent of GR (TEGR), which relies on spacetime torsion; and the Symmetric Teleparallel Equivalent of GR (STEGR), grounded in nonmetricity. Recent studies demonstrate that GR, TEGR, and STEGR are dynamically equivalent, raising questions about the fundamental structure of spacetime, the under-determination of these theories, and whether empirical distinctions among them are possible.
The aim of this work is to show that they are equivalent in many features but not exactly in everything. In particular, their relationship with the Equivalence Principle (EP) is different. The EP is a deeply theory-laden assumption, which is assumed as fundamental in constructing GR, with significant implications for our understanding of spacetime. However, it introduces unresolved conceptual issues, including its impact on the nature of the metric and connection, its meaning at the quantum level, tensions with other fundamental interactions and new physics, and its role in dark matter and dark energy problems.
In contrast, TEGR and STEGR recover the EP, in particular in its strong formulation, but do not rely on it as a foundational principle. The fact that GR, TEGR, and STEGR are equivalent in non-trivial predictions, but the EP is not necessary for TEGR and STEGR, suggests that it may not be a fundamental feature but an emergent one, potentially marking differences in the empirical content of the three theories.
Thus, the developments within the Geometric Trinity framework challenge traditional assumptions about spacetime and may help to better understand some of the unresolved foundational difficulties related to the EP.

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Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Mancini, Christian christian.mancini@na.infn.it Tino, Guglielmo Maria guglielmo.tino@unifi.it Capozziello, Salvatore salvatore.capozziello@na.infn.it
Additional Information:	Received: 19 January 2025. Accepted: 28 July 2025
Keywords:	General Relativity, Theories of Gravity, Equivalence Principle, Spacetime
Subjects:	Specific Sciences > Physics > Cosmology Specific Sciences > Physics > Relativity Theory
Depositing User:	Mr. Christian Mancini
Date Deposited:	01 Sep 2025 12:36
Last Modified:	01 Sep 2025 12:36
Item ID:	26423
Journal or Publication Title:	Foundations of Physics
Publisher:	Springer
Official URL:	https://doi.org/10.1007/s10701-025-00882-x
DOI or Unique Handle:	10.1007/s10701-025-00882-x
Subjects:	Specific Sciences > Physics > Cosmology Specific Sciences > Physics > Relativity Theory
Date:	28 August 2025
Volume:	55
Number:	69
URI:	https://philsci-archive.pitt.edu/id/eprint/26423

Available Versions of this Item

• Equivalent Gravities and Equivalence Principle: Foundations and experimental implications. (deposited 10 Jan 2025 16:20)
  • Equivalent Gravities and Equivalence Principle: Foundations and experimental implications. (deposited 29 Aug 2025 13:13)
    • Equivalent Gravities and Equivalence Principle: Foundations and experimental implications. (deposited 01 Sep 2025 12:36) [Currently Displayed]
  • Equivalent Gravities and Equivalence Principle: Foundations and experimental implications. (deposited 19 May 2025 12:54)

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