The 'Geometric Trinity' claims general relativity, TEGR, and STEGR are dynamically equivalent despite resting on different geometric foundations

physicsphilosophy-of-physicsgravitygauge-theorygeometric-trinityunderdetermination

The Geometric Trinity (GT), a name given by Jiménez, Heisenberg and Koivisto (2019) to a cluster of results in classical gravitational theory, holds that three theories built from three different fundamental geometric attributes of spacetime — general relativity (curvature), the Teleparallel Equivalent of General Relativity (TEGR, torsion), and the Symmetric Teleparallel Equivalent of General Relativity (STEGR, non-metricity) — produce field equations that coincide. Kartik Tiwari's arXiv:2609.38292 restates the claim as describing "a trio of equivalent theories of gravity which are constructed exclusively using just one of the three possible, independent geometrical attributes of spacetime." Taken at face value, the equivalence implies it is impossible even in principle — not merely in practice — to determine from particle trajectories whether a given spacetime is curved, torsioned, or non-metric, a textbook case of theoretical underdetermination.

This note records GT's claim as Tiwari restates it on his way to challenging it; see claim-gauge-gravitys-hypermomentum-challenge-conditionally-breaks-geometric-trinity-equivalence for that challenge. The claim's actual origin is the 2019 Universe paper, a peer-reviewed venue not independently read this session — Tiwari's restatement is the only layer this note has checked.