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 gravitational metric theory of gravity f (χ) = χ 3/2 developed by . We show that the theory accounts in detail for two observational facts: (1) the phenomenology of flattened rotation curves associated to the Tully-Fisher relation observed in spiral galaxies, and (2) the details of observations of gravitational lensing in galaxies and groups of galaxies, without the need of any dark matter. We show how all dynamical observations on flat rotation curves and gravitational lensing can be synthesised in terms of the empirically required metric coefficients of any metric theory of gravity. We construct the corresponding metric components for the theory presented at second order in perturbation, which are shown to be perfectly compatible with the empirically derived ones. It is also shown that under the theory being presented, in order to obtain a complete full agreement with the observational results, a specific signature of Riemann's tensor has to be chosen. This signature corresponds to the one most widely used nowadays in relativity theory. Also, a computational program, the MEXICAS (Metric EXtended-gravity Incorporated through a Computer Algebraic System) code, developed for its usage in the Computer Algebraic System (CAS) Maxima for working out perturbations on a metric theory of gravity, is presented and made publicly available.

Modified Newtonian Dynamics as an Entropic Force

“…Small values of n yield soft transitions about the same point. For the case of spherically symmetric mass distribution, this extended Newtonian gravity approach proposal reproduces a MOND-like phenomenology [17] and has proven to be in good agreement with observations in astrophysical systems across different scales without invoking any dark matter component [4,5,8,9,14,15].…”

Astrophysical constraints and insights on extended relativistic gravity

“…As pointed out by Mendoza et al [14], recent observations have shown that gravitational lensing on individual [15][16][17][18][19], groups [20] and clusters of galaxies [21,22] can be modelled with the standard Schwarzschild solution of general relativity, assuming the existence of a total dark plus baryonic isothermal halo, where the Tully-Fisher law holds for the baryonic matter. As such, the bending angle of light can be calculated using the standard lensing equation, finding that it does not depend on the impact parameter and scales with the square root of the total baryonic mass.…”

MONDian dynamical modelling of NGC 288 with β ≠ 0

“…TeVeS of Bekenstein (2004), some of the F (R) theories, Capozziello & De Laurentis (2011), The extended Newtonian gravity of Mendoza et al (2011) or the covariant F (χ) of Mendoza et al (2013). For such theories, beyond a radius given by RM = (GM/a0) 1/2 , centrifugal equilibrium velocic 2015 RAS ties become flat at V = (GM a0) 1/4 .…”