On affine geometrical structure, generalized of Born Infeld models and Eddington's world conjectures

CIRILO-LOMBARDO, DIEGO JULIO

INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS

WORLD SCIENTIFIC PUBL CO PTE LTD

Año: 2022

0219-8878

In this work we give a detailed description and discussion of the dynamic gravitational equations of the model with lagrangian of the type ∫√(detR_{μν})d⁴x as proposed by Eddington time ago but with R_{μν} being a non Riemannian generalization of the Ricci tensor with the end to find the geometrical origin of the Eddington and Weyl conjectures concerning lagrangian densities (generalized volume) and natural gauge. The Ricci tensor in our case is particularly based in an affine geometry with a generalized compatibility condition previously proposed in mc and trace. Specifically we show that: i) the geometric action can be taken to a BI type form considering a totally antisymmetric torsion field, ii) Weyl´s proposal considering a universal gauge linked to a cosmological constant λ appears in the model naturally due of the proposed affine geometry, iii) the Eddington conjecture that establishes a relationship between metric and curvature or fundamental tensor with constant of proportionality λ (natural gauge) is geometrically verified in the model with generalized affine geometry.