Derivation of the 5D Einstein Field Equations from Lovelock's Uniqueness Theorem
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2026
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| _version_ | 1866901111843061760 |
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| author | Grčman, Igor |
| author_facet | Grčman, Igor |
| contents | <p>Paper 13 uses the 5D Einstein field equations G<span>AB </span>= 8πG<span>5 </span>T<span>AB </span>in over 40 locations (Israel conditions, interior BVP, bulk geometry, River flow, appendices). This equation was inherited from Book 1, Ch. 0 as a hidden postulate. We derive it from P1 (5D Lorentzian manifold) plus Lovelock’s naturalness conditions (1971).</p> <p>Lovelock’s theorem states that in D= 5 the most general second-order, symmetric, divergence-free, local tensor built from the metric is a linear combination of the Einstein tensor, a cosmological constant, and the Gauss–Bonnet tensor. We show that the Gauss–Bonnet contribution is suppressed by (ℓ<span>P</span>/R<span>ξ</span>)<span>2 </span>∼10<span>−34 </span>in the EDC regime, yielding pure Einstein equations to extraordinary precision. The epistemic status upgrades from hidden <span>[P] </span>to <span>[Der]</span>|P1+Lovelock, with two explicit naturalness assumptions <span>[P-nat]</span>: the equivalence principle (metric is dynamical) and Ostrogradsky stability (field equations are second-order). Both are weaker than postulating “5D Einstein holds.”</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19199358 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Derivation of the 5D Einstein Field Equations from Lovelock's Uniqueness Theorem Grčman, Igor Elastic Diffusive Cosmology 5D Einstein equations Lovelock theorem Gauss-Bonnet suppression field equations derivation second-order field equations 5D gravity <p>Paper 13 uses the 5D Einstein field equations G<span>AB </span>= 8πG<span>5 </span>T<span>AB </span>in over 40 locations (Israel conditions, interior BVP, bulk geometry, River flow, appendices). This equation was inherited from Book 1, Ch. 0 as a hidden postulate. We derive it from P1 (5D Lorentzian manifold) plus Lovelock’s naturalness conditions (1971).</p> <p>Lovelock’s theorem states that in D= 5 the most general second-order, symmetric, divergence-free, local tensor built from the metric is a linear combination of the Einstein tensor, a cosmological constant, and the Gauss–Bonnet tensor. We show that the Gauss–Bonnet contribution is suppressed by (ℓ<span>P</span>/R<span>ξ</span>)<span>2 </span>∼10<span>−34 </span>in the EDC regime, yielding pure Einstein equations to extraordinary precision. The epistemic status upgrades from hidden <span>[P] </span>to <span>[Der]</span>|P1+Lovelock, with two explicit naturalness assumptions <span>[P-nat]</span>: the equivalence principle (metric is dynamical) and Ostrogradsky stability (field equations are second-order). Both are weaker than postulating “5D Einstein holds.”</p> |
| title | Derivation of the 5D Einstein Field Equations from Lovelock's Uniqueness Theorem |
| topic | Elastic Diffusive Cosmology 5D Einstein equations Lovelock theorem Gauss-Bonnet suppression field equations derivation second-order field equations 5D gravity |
| url | https://doi.org/10.5281/zenodo.19199358 |