We study disc galaxies in the framework of General Relativity to focus on the possibility that, even in the low energy limit, there are relevant corrections with respect to the purely Newtonian approach. Our analysis encompasses the model both considering a low energy expansion and exact solutions, making it clear the connection between these different approaches. In particular, we focus on two different limits: the well known gravitomagnetic analogy and a new limit, called strong gravitomagnetism, which has corrections in c of the same order as the Newtonian terms. We show that these two limits of the general class of solution can account for the observed flat velocity profile, contrary to what happens using Newtonian models, where a dark matter contribution is required. Hence, we suggest a geometrical origin for a certain amount of dark matter effects.
The geometrical nature of gravity emerges from the universality dictated by the equivalence principle. In the usual formulation of General Relativity, the geometrisation of the gravitational interaction is performed in terms of the spacetime curvature, which is now the standard interpretation of gravity. However, this is not the only possibility. In these notes we discuss two alternative, though equivalent, formulations of General Relativity in flat spacetimes, in which gravity is fully ascribed either to torsion or to non-metricity, thus putting forward the existence of three seemingly unrela…
The geometrical argument of the general relativity principle of Einstein is formulated in unstable Riemann space-time just inspired by the nonlinear representation of supersymmetry, which produces new Einstein-Hilbert type action.
The Chrono'Geometrical Structure of Special and General Relativity: Towards a Background-Independent Description of the Gravitational Field and Elementary Particles
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-time, no general principle is supposed. The properties we impose to some domains of (M, g) are only simple geometric constraints, essentially based on the concept of "curvature". These geometric properties allow to define, depending on considered cases, some objects (frequently d…
General Relativity enjoys the freedom of different geometrical interpretations in terms of curvature, torsion or non-metricity. Within this geometrical trinity, a simpler geometrical formulation of General Relativity manifests itself in the latter, where gravity is entirely attributed to non-metricity. In this Letter, we consider non-linear extensions of Coincident General Relativity $f(\mathring{\mathbb{Q}})$ for phenomenological applications on both cosmological as well as galactic scales. The theory not only delivers dark energy on large scales but also recovers MOND on galactic scales, tog…
It is known that recently proposed model of mimetic gravity can be presented as general relativity with an additional mimetic matter. We discuss a possibility to analogously reformulate the embedding theory, which is the geometrical description of gravity proposed by Regge and Teitelboim, treating it also as general relativity with some additional matter. We propose a form of action which allows to describe this matter in terms of conserved currents. This action turns out to be a generalization of the perfect fluid action, which can be useful in the analysis of the properties of the additional…
The existence of stationary solutions of the Einstein-Vlasov-Maxwell system which are axially symmetric but not spherically symmetric is proven by means of the implicit function theorem on Banach spaces. The proof generalises the methods of an article by Håkan Andréasson, Markus Kunze and Gerhard Rein where a similar result is obtained for uncharged particles. Among the solutions constructed in this article there are rotating and non-rotating ones. Static solutions exhibit an electric but no magnetic field. In the case of rotating solutions, in addition to the electric field, a purely poloidal…
All energy is gravitational energy. That is the consequence of the equivalence principle, according to which gravity is the universal interaction. The physical charges of this interaction have remained undisclosed, but the Adventof the Geometrical Trinity opened a new approach to this foundational problem. Here it is shown to provide a background-independent unification of the previous, non-covariant approaches of Bergmann-Thomson, Cooperstock, Einstein, von Freud, Landau-Lifshitz, Papapetrou and Weinberg. First, the Noether currents are derived for a generic Palatini theory of gravity coupled…
We study the geometrical-optics expansion for circularly-polarized electromagnetic waves propagating on a curved spacetime in general relativity. We show that higher-order corrections to the Faraday and stress-energy tensors may be found via a system of transport equations, in principle. At sub-leading order, the stress-energy tensor possesses terms proportional to the wavelength whose sign depends on the handedness of the circular polarization. Due to such terms, the direction of energy flow is not aligned with the gradient of the eikonal phase, in general, and the wave may carry a transverse…
Since the first appearance of general relativity in 1916, various experiments have been conducted to test the theory. Due to the weakness of the interactions involved, all of the documented tests were carried out in a gravitational field generated by objects of an astronomical scale. We propose an idea for an experiment that could detect purely general-relativistic effects in a lab-generated gravitational field. It is shown that a set of dense rapidly-revolving cylinders produce a frame-dragging effect substantial enough to be two orders of magnitude away from the observable range of the next …
Within the framework of $f(R)=R+αR^2$ gravity, we study realistic models of neutron stars, using equations of state compatible with the LIGO constraints. i.e. APR4, MPA1, SLy, and WW1. By numerically solving modified Tolman-Oppenheimer-Volkoff equations, we investigate the Mass--Radius relation in both metric and torsional $f(R)=R+αR^2$ gravity models. In particular, we observe that torsion effects decrease the compactness and total mass of neutron star with respect to the General Relativity predictions, therefore mimicking the effects of a repulsive massive field. The opposite occurs in the m…
