Kinetic theory of collisionless self-gravitating gases. II. Relativistic corrections in galactic dynamics

Abstract

In this paper we study the kinetic theory of many-particle astrophysical systems imposing axial symmetry and extending our previous analysis in Phys. Rev. D 83, 123007 (2011).Starting from a Newtonian model describing a collisionless self-gravitating gas, we develop a framework to include systematically the first general relativistic corrections to the matter distribution and gravitational potentials for general stationary systems. Then, we use our method to obtain particular solutions for the case of the Morgan & Morgan disks. The models obtained are fully analytical and correspond to the post-Newtonian generalizations of classical ones. We explore some properties of the models in order to estimate the importance of post-Newtonian corrections and we find that, contrary to the expectations, the main modifications appear far from the galaxy cores. As a by-product of this investigation we derive the corrected version of the tensor virial theorem. For stationary systems we recover the same result as in the Newtonian theory. However, for time dependent backgrounds we find that there is an extra piece that contributes to the variation of the inertia tensor.

A method for evaluating models that use galaxy rotation curves to derive the density profiles

“…These small numbers suggest that GR corrections to Newtonian dynamics, namely on the rotation curve (RC), are smaller than 1%, and therefore significantly smaller than the typical uncertainties associated with the astrophysical data from galaxies. Some authors agree with the assumption of using GR in galaxies (item i), but found that those small numbers in the items ii and iii may lead to significative consequences on dark matter distribution in galaxies and corrections to the RCs larger than 10% (Cooperstock & Tieu 2007;Carrick & Cooperstock 2012;Magalhaes & Cooperstock 2015;Balasin & Grumiller 2008;Ramos-Caro et al 2012). The CT approach (Cooperstock & Tieu 2006Carrick & Cooperstock 2012;Magalhaes & Cooperstock 2015) has received a number of criticisms on the theoretical basis, which the authors claim to have answered (Carrick & Cooperstock 2012).…”

On the rotation curves for axially symmetric disc solutions of the Vlasov–Poisson system

“…González, Plata & Ramos-Caro (2010) start from the observational data of four galaxies and construct models with the corresponding densities and potentials. The effects of relativistic corrections are studied in (Ramos-Caro, Agn & Pedraza 2012, Nguyen & Lingam 2013, and a model motivated by renormalization group corrections is investigated in (Rodrigues, Letelier & Shapiro 2010). Rotation curves obtained in alternative gravitational theories such as Modified Newtonian Dynamics (MOND) and Scalar-Tensor-Vector Gravity (STVG) can be found in (Famaey & McGaugh 2012) The outline of the present paper is as follows.…”

Vertical stability of circular orbits in relativistic razor-thin disks

“…The stability of circular geodesics in smooth axially symmetric stress-energy distributions was first considered in [12], in which some remarks about their vertical stability in the limit of an infinitesimally thin disk are presented. During the last decades, many exact solutions representing thin disks were obtained, both in GR (see for example [13][14][15][16][17][18][19][20] and the reviews [4,5]) and in modified theories of gravity [21,22], mainly based * rss.vieira@usp.br † javier@ufscar.br ‡ asaa@ime.unicamp.br on the formalism of distribution-valued curvature tensors proposed by Taub [23]. For razor-thin disks, such an approach is consistent with the results about distributional sources in general relativity obtained by Geroch and Traschen [24], which provide an adequate framework to deal with distribution-valued curvature tensors with support on spacetime hypersurfaces.…”