Relativistic rotation curve for cosmological structures (original) (raw)
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Using a general relativistic exact model for spherical structures in a cosmological background, we have calculated the test particle geodesics within the structure for different masses in order to obtain the velocity profile of stars or galaxies. Defining a Newtonian mass based on the classical dynamical relations, it turns out that the Misner-Sharp quasi-local mass is almost equal to the Newtonian one. This, however, is not the case for other general relativistic quasi-local mass definitions, which can be much smaller than the mass definition based on the classical dynamics. Therefore, based on the rotation curve, we are not in a position to relate a unique mass to a cosmological structure within general relativity even in cases of very weak gravity.
A galactic spacetime model to resolve the problem between mass density and rotation curve
In the present paper, we introduce a spacetime model where the particle circular motions have the characteristics of the galaxy rotation curves. We calculate the Einstein tensor and analyze the mass density-radius relation. We find that near the core the density-radius relation follows inverse fourth-power law, and near the edge it follows the Schechter function, which just like a luminous mass density profile of a real galaxy. In the other words, our result shows that only general relativity without dark matter may be enough to explain the galaxy rotation curves.
Relativistic models of galaxies
Monthly Notices of the Royal Astronomical Society, 2005
A special form of the isotropic metric in cylindrical coordinates is used to construct what may be interpreted as the general relativistic versions of some well-known potential-density pairs used in Newtonian gravity to model three-dimensional distributions of matter in galaxies. The components of the energy-momentum tensor are calculated for the first two Miyamoto-Nagai potentials and a particular potential due to Satoh. The three potentials yield distributions of matter in which all tensions are pressures and all energy conditions are satisfied for certain ranges of the free parameters. A few non-planar geodesic orbits are computed for one of the potentials and compared with the Newtonian case. Rotation is also incorporated in the models and the effects of the source rotation on the rotation profile are calculated as first-order corrections by using an approximate form of the Kerr metric in isotropic coordinates.
Orbit of a Test Particle and Rotation Curves of Galaxies in an Expanding Universe
A new equation of motion, which is derived in an accompanying article by considering spacetime measurement via geometrodynamic clocks, is surveyed. It is shown that the new term in the equation of motion suggest a small correction in orbits of outer planets; thus it is compatible with the solar system data. Then a typical system of particles is investigated to have a better understanding of galactic structures and the general form of the force law is introduced. As the first example, rotation curve and mass discrepancy functions of an axisymmetric disk of stars are derived. It is shown that the general form of rotation curve could be justified. In addition, it is suggested that the mass discrepancy as a function of centripetal acceleration becomes significant near $ a_{0} .Animportantfeatureofthismodelisthepredictionofaconstantaccelerationinouterpartsofgalaxies.Thecriticalsurfacedensity,. An important feature of this model is the prediction of a constant acceleration in outer parts of galaxies. The critical surface density, .Animportantfeatureofthismodelisthepredictionofaconstantaccelerationinouterpartsofgalaxies.Thecriticalsurfacedensity, \sigma_{0}=a_{0}/G ,hasasignificantroleinrotationcurveandmassdiscrepancyplots.ThespecificformofNFWmassdensityprofileatsmallradii,, has a significant role in rotation curve and mass discrepancy plots. The specific form of NFW mass density profile at small radii, ,hasasignificantroleinrotationcurveandmassdiscrepancyplots.ThespecificformofNFWmassdensityprofileatsmallradii, \rho \propto 1/r $, is explained too.
Galactic Dynamics via General Relativity: A Compilation and New Developments
International Journal of Modern Physics A, 2007
We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite of the weak gravitational field and the non-relativistic source velocities, the mathematical system is still seen to be non-linear. It is shown that the rotation curves for various galaxies as examples are consistent with the mass density distributions of the visible matter within essentially flattened disks. This obviates the need for a massive halo of exotic dark matter. We determine that the mass density for the luminous threshold as tracked in the radial direction is 10 −21.75 kg·m −3 for these galaxies and conjecture that this will be the case for other galaxies yet to be analyzed. We present a velocity dispersion test to determine the extent, if of any significance, of matter that may lie beyond the visible/HI region. Various comments and criticisms from colleagues are addressed.
Galactic rotation dynamics in a new f(R) gravity model
arXiv (Cornell University), 2022
We propose to test the viability of the recently introduced f (R) gravity model in the galactic scales. For this purpose we consider test particles moving in stable circular orbits around the galactic center. We study the Palatini approach of f (R) gravity via Weyl transformation, which is the frame transformation from the Jordan frame to the Einstein frame. We derive the expression of rotational velocities of test particles in the new f (R) gravity model. For the observational data of samples of high surface brightness and low surface brightness galaxies, we show that the predicted rotation curves are well fitted with observations, thus implying that this model can explain flat rotation curves of galaxies. We also study an ultra diffuse galaxy, AGC 242019 which has been claimed in literature to be a dark matter dominated galaxy similar to low surface brightness galaxies with a slowly rising rotation curve. The rotation curve of this galaxy also fits well with the model prediction in our study. Furthermore, we studied the Tully-Fisher relation for the entire sample of galaxies and found that the model prediction shows the consistency with the data.
On galaxy rotation curves from a continuum mechanics approach to modified gravity
International Journal of Modern Physics D
We consider a modification of General Relativity motivated by the treatment of anisotropies in Continuum Mechanics. The Newtonian limit of the theory is formulated and applied to galactic rotation curves. By assuming that the additional structure of spacetime behaves like a Newtonian gravitational potential for small deviations from isotropy, we are able to recover the Navarro–Frenk–White profile of dark matter halos by a suitable identification of constants. We consider the Burkert profile in the context of our model and also discuss rotation curves more generally.
International Letters of Chemistry, Physics and Astronomy, Vol. 78, pp. 39-50, 2018
For the relativistic uniform system with an invariant mass density the exact expressions are determined for the potentials and strengths of the gravitational field, the energy of particles and fields. It is shown that, as in the classical case for bodies with a constant mass density, in the system with a zero vector potential of the gravitational field, the energy of the particles, associated with the scalar field potential, is twice as large in the absolute value as the energy defined by the tensor invariant of the gravitational field. The problem of inaccuracy of the use of the field's stress-energy tensors for calculating the system's mass and energy is considered. The found expressions for the gravitational field strengths inside and outside the system allow us to explain the occurrence of the large-scale structure of the observable Universe, and also to relate the energy density of gravitons in the vacuum field with the limiting mass density inside the proton. Both the Universe and the proton turn out to be relativistic uniform systems with the maximum possible parameters. The described approach allows us to calculate the maximum possible Lorentz factor of the matter particles at the center of the neutron star and at the center of the proton, and also to estimate the radius of action of the strong and ordinary gravitation in cosmological space.