On the galactic rotation curves problem within an axisymmetric approach

Abstract

In U. Nucamendi et al. Phys. Rev. D63 (2001) 125016 and K. Lake, Phys. Rev. Lett. 92 (2004) 051101 it has been shown that galactic potentials can be kinematically linked to the observed red/blue shifts of the corresponding galactic rotation curves under a minimal set of assumptions: the emitted photons come from stable timelike circular geodesic orbits of stars in a static spherically symmetric gravitational field, and propagate to us along null geodesics. It is remarkable that this relation can be established without appealing at all to a concrete theory of gravitational interaction. Here we generalize this kinematical spherically symmetric approach to the galactic rotation curves problem to the stationary axisymmetric realm since this is precisely the symmetry that spiral galaxies possess. Thus, by making use of the most general stationary axisymmetric metric, we also consider stable circular orbits of stars that emit signals which travel to a distant observer along null geodesics and express the galactic red/blue shifts in terms of three arbitrary metric functions, clarifying the contribution of the rotation as well as the dragging of the gravitational field. This stationary axisymmetric approach distinguishes between red and blue shifts emitted by circularly orbiting receding and approaching stars, respectively, even when they are considered with respect to the center of a spiral galaxy, indicating the need of precise measurements in order to confront predictions with observations. We also point out the difficulties one encounters in the attempt of determining the metric functions from observations and list some possible strategies to overcome them.

7 pages in latex (MNRAS format), no figures, discussion and references added

References in corpus (15)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• The Universal Rotation Curve of Spiral Galaxies. II The Dark Matter Distribution out to the Virial Radius
• Dark matter as a geometric effect in f(R) gravity
• Wide binaries as a critical test of Classical Gravity
• Rings and shells of "dark matter" as MOND artifacts
• General relativistic velocity: the alternative to dark matter
• A natural approach to extended Newtonian gravity: tests and predictions across astrophysical scales
• Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
• General relativistic dynamics applied to the rotation curves of galaxies
• General Relativity Resolves Galactic Rotation Without Exotic Dark Matter
• Finite thin disc models of four galaxies in the Ursa Major cluster: NGC3877, NGC3917, NGC3949 and NGC4010
• Singular disk of matter in the Cooperstock-Tieu galaxy model
• Just dust : About the (in)applicability of rotating dust solutions as realistic galaxy models
• General Relativistic Galaxy Rotation Curves: Implications for Dark Matter Distribution
• On the stability criteria for equatorial circular orbits in Galactic Dynamics: I.Newtonian Thin Disks

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