Relativistic rotation curve for cosmological structures

TL;DR

This paper develops a general relativistic model to compute rotation curves of cosmological structures, showing that relativistic and Newtonian curves are nearly identical despite differences in mass definitions.

Contribution

It introduces an algorithm for calculating geodesics in relativistic structures, providing a new way to derive rotation curves independent of mass definitions.

Findings

Relativistic rotation curves closely match Newtonian ones for toy and NFW profiles.

Mass estimates differ significantly between relativistic and Newtonian models.

The method offers a mass-independent approach to galaxy rotation profiles.

Abstract

Using a general relativistic exact model for spherical structures in a cosmological background, we have put forward an algorithm to calculate the test particle geodesics within such cosmological structures in order to obtain the velocity profile of stars or galaxies. The rotation curve thus obtained is based on a density profile and is independent of any mass definition which is not unique in general relativity. It is then shown that this general relativistic rotation curves for a toy model and a NFW density profile are almost identical to the corresponding Newtonian one, although the general relativistic masses may be quite different.