Exact Solutions with Asymptotically Flat Galactic Rotation Curves

Abstract

We present a new set of spacetime solutions for spiral galaxies corresponding to flat rotation curves at large distances. These correspond to anisotropic pressure, which could be sourced by either matter or geometry. As examples, we elucidate the galactic metrics corresponding to the non-ideal generalizations of `dust' and `radiation', respectively. Further, we find a dynamical realization of the Einstein cluster when the spatially averaged equation of state (w) happens to be non-zero but small. The correction to the Einsteinian bending angle for a light ray penetrating a large galactic halo is predicted to be: $(2+3w)\pi v^2/(1+3w)c^2$, v being the limiting rotational velocity. We infer a mild decline of the rotation curves ($v^{\prime }(r)1/r^2$) at large radii for sufficiently luminous galaxies, as also indicated by some specific observations.

22 pages; Identical with published version

References in corpus (15)

• A History of Dark Matter
• Is the Lightest Kaluza-Klein Particle a Viable Dark Matter Candidate?
• Scalar-Tensor-Vector Gravity Theory
• The Circular Velocity Curve of the Milky Way from $5$ to $25$ kpc
• The distribution of dark matter in galaxies
• Can the galactic rotation curves be explained in brane world models?
• Galactic Potentials
• An $f(R)$ gravitation for galactic environments
• Modelling galaxy halos using dark matter with pressure
• Mapping the Milky Way Disk with Gaia DR3: 3D extended kinematic maps and rotation curve to $\approx 30$ kpc
• Can extra dimensional effects replace dark matter ?
• Gravitational waves and lensing of the metric theory proposed by Sobouti
• Gravitational lensing in braneworld gravity: formalism and applications
• Gravity theory with a dark extra dimension
• 4D Einstein-Gauss-Bonnet Gravity From Non-Einsteinian Phase