Jacobson's Thermodynamic Approach to Classical Gravity Applied to Non‐Riemannian Geometries: Remarks on the Simplicity of Nature

ABSTRACT Three decades ago, Ted Jacobson surprised us with a very appealing approach to classical gravity. According to him, the gravitational field equations are the consequence of the first law of thermodynamics applied to a Rindler observer. Jacobson's approach, being formulated for Riemannian geometries, we have wondered what its consequences would be for non‐Riemannian geometries. The results of our quest have been particularly appealing: we have found that the theory that derives from the Einstein‐Hilbert action, arguably “the simplest one,” does not belong to the pool of gravitational theories available for Nature's selection (except in the Riemannian case). In the search for a unique alternative, we have considered the hypotheses employed in the formulation of the Lanczos‐Lovelock theories of gravity. Together, the two approaches point toward the theory that derives from the Einstein‐Hilbert action plus a term quadratic in the torsion vector as the one that would be selected by Nature in the non‐Riemannian case without non‐metricity (when the energy‐momentum tensor is identified as its metric version). The same strategy cannot be followed in the full non‐Riemannian case (and in the previous case when the energy‐momentum tensor is identified as its canonical version) as the two approaches are mutually inconsistent.