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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.00422 |
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| _version_ | 1866911722330128384 |
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| author | Martinez, Jhan N. Rodriguez-Ruiz, Jose F. Rodriguez, Yeinzon |
| author_facet | Martinez, Jhan N. Rodriguez-Ruiz, Jose F. Rodriguez, Yeinzon |
| contents | 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 of a unique alternative, we have considered the hypotheses employed in the formulation of the Lanczos-Lovelock theories of gravity. Together, the two approaches point towards 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00422 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature Martinez, Jhan N. Rodriguez-Ruiz, Jose F. Rodriguez, Yeinzon General Relativity and Quantum Cosmology High Energy Physics - Theory Popular Physics 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 of a unique alternative, we have considered the hypotheses employed in the formulation of the Lanczos-Lovelock theories of gravity. Together, the two approaches point towards 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. |
| title | Jacobson's thermodynamic approach to classical gravity applied to non-Riemannian geometries: remarks on the simplicity of Nature |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Popular Physics |
| url | https://arxiv.org/abs/2602.00422 |