2015/05/12 by Waldyr A. Rodrigues, Rodrigues, Waldyr A., Samuel A. Wainer +1
Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #FOS: Physical sciences #Mathematical Physics (math-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1505.02935
openalex publication_date 2015/05/12 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28
We discuss the physics of interacting tensor fields and particles living in\nM=\S0(1,4)/\S0 (1,3)\≃\ℝ\× S3 a\nsubmanifold of mathringM=(\ℝ5, boldsymbol mathringg), where\n boldsymbol mathring g has signature (1,4). Structure\n(M, boldsymbolg) where ( boldsymbolg=i\∗ boldsymbol mathringg)\nis a Lorentzian manifold. Structure\n(M, boldsymbolg,\τ_ boldsymbolg, uparrow) is primely used to study\nthe energy-momentum conservation law (for a system of physical fields (and\nparticles) living in M and to get the respective equations of motion. We\nconstruct two different de Sitter spacetime structures\nMdSL=(M, boldsymbolg,D,\τ_ boldsymbolg, uparrow) and\nMdSTP=(M, boldsymbolg,\∇,\τ_ boldsymbolg , uparrow). Both\n(metrical compatible) connections are used only as mathematical devices. In\nparticular MdSL is not supposed to be the model of any gravitational field\nin the(\GRT). We clarify some misconceptions appearing in the\nliterature. We use the Clifford and spin-Clifford bundles formalism and gives a\nthoughtful presentation of the concept of a Komar current \JA (in\nGRT) associated to any vector field \A. A formula for the Komar\ncurrent and its physical meaning are given. We show also how F=dA satisfy in\nthe Clifford bundle a Maxwell like equation encoding the contents of Einstein\nequation. We show that in GRT there are infinitely many conserved\ncurrents,independently of the fact that the Lorentzian spacetime possess or not\nKilling vector fields and that even when the appropriate Killing vector fields\nexist there does not exist a conserved energy-momentum covector (not a covector\nfield) as in SRT.\n