Gravitational lensing with f (χ) = χ3/2 gravity in accordance with astrophysical observations

Abstract

In this article we perform a second order perturbation analysis of the\ngravitational metric theory of gravity $ f(\\chi) = \\chi^{3/2} $ developed by\nBernal et al. (2011). We show that the theory accounts in detail for two\nobservational facts: (1) the phenomenology of flattened rotation curves\nassociated to the Tully-Fisher relation observed in spiral galaxies, and (2)\nthe details of observations of gravitational lensing in galaxies and groups of\ngalaxies, without the need of any dark matter. We show how all dynamical\nobservations on flat rotation curves and gravitational lensing can be\nsynthesised in terms of the empirically required metric coefficients of any\nmetric theory of gravity. We construct the corresponding metric components for\nthe theory presented at second order in perturbation, which are shown to be\nperfectly compatible with the empirically derived ones. It is also shown that\nunder the theory being presented, in order to obtain a complete full agreement\nwith the observational results, a specific signature of Riemann's tensor has to\nbe chosen. This signature corresponds to the one most widely used nowadays in\nrelativity theory. Also, a computational program, the MEXICAS (Metric\nEXtended-gravity Incorporated through a Computer Algebraic System) code,\ndeveloped for its usage in the Computer Algebraic System (CAS) Maxima for\nworking out perturbations on a metric theory of gravity, is presented and made\npublicly available.\n