2021/07/17 by Juliana Osorio Morales, Osvaldo P. Santillán, Morales, Juliana Osorio +1
Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.2107.08269
openalex publication_date 2021/07/17 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
As is known from studies of gravity models in the Palatini formalism, there\nexist two inequivalent definitions of the generalized Ricci tensor in terms of\nthe generalized curvature namely, widetildeR\μ\ν=R^\ρ\μ\ρ\ν\nand R^\μ\ν=g\α\βR^\μ\α\ν\β. A deep formal\ninvestigation of theories with lagrangians of the form\nL=L( widetildeR(\μ\ν)) was initiated in [4]. In that work, the authors\nleave the connection free, and find out that the torsion only appears as a\nprojective mode. This agrees with the widely employed condition of vanishing\ntorsion in these theories as a simple gauge choice. In the present work the\ncomplementary scenario is studied namely, the one described by a lagrangian\nthat depends on the other possible Ricci tensor L=L(R(\μ\ν)). The\ntorsion is completely characterized in terms of the metric and the connection,\nand a rather detailed description of the equations of motion is presented. It\nis shown that these theories are non trivial even for 1+1 space time\ndimensions, and admit non zero torsion even in this apparently simple case. It\nis suggested that to impose zero torsion by force may result into an\nincompatible system. In other words, the presence of torsion may be beneficial\nfor insuring that the equations of motion are well posed. The results presented\nhere do not contradict the results of [4], as the resulting theories are\ninequivalent.\n