Exact solutions for differentially rotating galaxies in general relativity

Understand

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.