Exact solutions for differentially rotating galaxies in general relativity

Abstract: Two classes of stationary axisymmetric solutions of Einstein's equations for isolated differentially rotating matter sources are presented. The asymptotic regime is extracted, with attention to quasilocal gravitational energy, shear and angular momentum related by the Raychaudhuri equation. At outer boundaries the quasilocal angular momentum and energy densities vanish, defining novel geometric structures - the vortex surface and the rotosurface. Solutions with a rotosurface present a new notion of asymptotic flatness: vorticity, shear and Kretschmann scalars vanish at a finite radial distance from the symmetry centre. Synthetic rotation curves for the Milky Way are presented, fit to GAIA-DR3 data, and potential astrophysical signatures are suggested. Whether or not abundant collisionless dark matter exists, the new solutions very strongly support suggestions that the phenomenology of galactic rotation curves be fundamentally reconsidered, for consistency with general relativity.