Relativistic models of galaxies (original) (raw)
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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.
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.
Relativistic rotation curve for cosmological structures
International Journal of Modern Physics D, 2014
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.
The late time accelerated expansion of the Universe demands that even in local galactic scales it is desirable to study astrophysical phenomena, particularly relativistic accretion related phenomena in massive galaxies or in galaxy mergers and the dynamics of the kiloparsecs-scale structure and beyond, in the local galaxies in Schwarzschild–de Sitter (SDS) background, rather than in Schwarzschild or Newtonian paradigm. Owing to the complex and nonlinear character of the underlying magnetohydrodynamical equations in general relativistic (GR) regime, it is quite useful to have a Newtonian analogous potential containing all the important GR features that allows us to treat the problem in Newtonian framework for study of accretion and its related processes. From the principle of conserved Hamiltonian of the test particle motion, here, a three dimensional Newtonian analogous potential has been obtained in spherical geometry corresponding to SDS/Schwarzschild–anti–de Sitter spacetime, tha...
Three-dimensional axisymmetric sources for Majumdar–Papapetrou type spacetimes
International Journal of Modern Physics D, 2018
From Newtonian potential-density pairs, we construct three-dimensional axisymmetric relativistic sources for a Majumdar–Papapetrou type conformastatic spacetime. As simple examples, we build two families of relativistic thick disks from the first two Miyamoto–Nagai potential-density pairs used in Newtonian gravity to model flat galaxies, and a three-component relativistic model of galaxy (bulge, disk and dark matter halo). We study the equatorial circular motion of test particles around such structures. Also the stability of the orbits is analyzed for radial perturbation using an extension of the Rayleigh criterion. In all examples, the relativistic effects are analyzed and compared with the Newtonian approximation. The models are considered satisfying all the energy conditions.
Anisotropic relativistic stellar models
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the anisotropy factor. The energy density and both radial and tangential pressures are finite and positive inside the anisotropic star. Numerical results show that the basic physical parameters (mass and radius) of the model can describe realistic astrophysical objects like neutron stars.
Astrophysics and Space Science, 2014
In this paper we have studied a particular class of exact solutions of Einstein's gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, R c GM 2 , can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538−52, LMC X-4, SAX J1808.4−3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.
Rotation Curves of Galaxies by Fourth Order Gravity
We investigate the radial behavior of galactic rotation curves by a Fourth Order Gravity adding also the Dark Matter component. The Fourth Order Gravity is a theory of Gravity described by Lagrangian generalizing the one of Hilbert Einstein containing a generic function of the Ricci scalar, the Ricci and Riemann tensor. A systematic analysis of rotation curves, in the Newtonian Limit of theory, induced by all galactic sub-structures of ordinary matter is shown. This analysis is presented for Fourth Order Gravity with and without Dark Matter. The outcomes are compared with respect to the classical outcomes of General Relativity. The gravitational potential of point-like mass is the usual potential corrected by two Yukawa terms. The rotation curve is higher or also lower than curve of General Relativity if in the Lagrangian the Ricci scalar square is dominant or not with respect to the contribution of the Ricci tensor square. The theoretical spatial behaviors of rotation curve are compared with the experimental data for the Milky Way and the galaxy NGC 3198. Although the Fourth Order Gravity gives more rotational contributions, in the limit of large distances the Keplerian behavior is ever present, and it is missing only if we add the Dark Matter component. However by modifying the theory of Gravity, consequently, also the spatial description of Dark Matter could undergo a modification and the free parameters of model can assume different values. After an analytical discussion of theoretical behaviors and the comparing with experimental evidence we can claim that any Fourth Order Gravity is not successful to explain the galactic rotation curves. In the last part of paper we analyze the gravitational potential induced by Lagrangian containing only powers of Ricci scalar. In this case we find an inconsistency in the boundary conditions in the passage from matter to the vacuum.
We obtain a class of solutions to the Einstein–Maxwell equations describing charged static spheres. Upon specifying particular forms for one of the gravitational potentials and the electric field intensity, the condition for pressure isotropy is transformed into a hypergeometric equation with two free parameters. For particular parameter values we recover uncharged solutions corresponding to specific neutron star models. We find two charged solutions in terms of elementary functions for particular parameter values. The first charged model is physically reasonable and the metric functions and thermodynamic variables are well behaved. The second charged model admits a negative energy density and violates the energy conditions.
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.