Visualisation of counter-rotating dust disks using ray tracing methods

Abstract

Physical aspects of stationary axisymmetric vacuum spacetimes given by exact solutions of the Einstein equations are discussed via ray tracing. A detailed study of the spacetime generated by a disk of counter-rotating dust is presented. The spacetime is given in explicit form in terms of hyperelliptic theta functions. The numerical approach to ray tracing is set up for general stationary axisymmetric spacetimes and tested at the well-studied example of the Kerr solution. Similar features as in the case of a rotating black hole, are explored in the case of a dust disk. The effect of the central redshift varying between a Newtonian disk and the ultrarelativistic disk, where the exterior of the disk can be interpreted as the extreme Kerr solution, and the transition from a single component disk to a static disk is explored. Frame dragging, as well as photon spheres, are discussed.