2009/07/14 by Eduardo A. Notte-Cuello, E. A. Notte-Cuello, R. da Rocha +3 · 5 citations
Mathematics · Physics and Astronomy · #Field (mathematics) #Field theory (psychology) #Gravitation #Gravitational field #Manifold (fluid mechanics) #Minkowski space #Poincaré conjecture #Quantum Electrodynamics and Casimir Effect #Quantum and Classical Electrodynamics #Realization (probability) #Relativity and Gravitational Theory #math-ph #math.MP
paper · pdf · open access · doi:10.4303/jpm/p100506
published in Journal of Physical Mathematics 2, 1-21 (OMICS Publishing Group)
arxiv created 2009/07/14 · openalex publication_date 2010/01/01 · arxiv updated 2014/11/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This paper shows how a gravitational field generated by a given energy-momentum\ndistribution (for all realistic cases) can be represented by distinct\ngeometrical structures (Lorentzian, teleparallel, and nonnull nonmetricity\nspacetimes) or that we even can dispense all those geometrical structures and\nsimply represent the gravitational field as a field in Faraday’s sense living in\nMinkowski spacetime. The explicit Lagrangian density for this theory is given,\nand the field equations (which are Maxwell’s like equations) are shown to be\nequivalent to Einstein's equations. Some examples are worked in detail in order\nto convince the reader that the geometrical structure of a manifold (modulus\nsome topological constraints) is conventional as already emphasized by Poincaré\nlong ago, and thus the realization that there are distinct geometrical\nrepresentations (and a physical model related to a deformation of the continuum\nsupporting Minkowski spacetime) for any realistic gravitational field strongly\nsuggests that we must investigate the origin of its physical nature. We hope\nthat this paper will convince readers that this is indeed the case.