Relativistic disks - II. Self-similar disks in rotation

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Abstract
Disks specified by a constant circular velocity V must have structures determined by the constants of gravitation theory and V. No length can be made from G, c and V, so a magnification of a solution must again be a solution, provided new units of time are also used. Thus disks specified by velocities alone are self-similar. The principle still holds for disks with velocity dispersion, provided these too are independent of radius. A general theory of self-similar axially-symmetrical structures is developed and applied to cold, flat, self-similar disks in rotation. All such structures are of infinite extent and of infinite total mass. At high velocities conical ergoregions develop about the disk and these grow until the cones close on the symmetry axis at V = 0.438 c. The behaviour of the simplest geodesies in the metrics is studied.

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