Relativistic disks as sources of the Kerr metric

Many spacetimes are known which should represent gravitational fields outside rotating sources, but for which no satisfactory sources have been found. We indicate that these spacetimes can arise as the metrics of counterrotating thin disks of finite mass, consisting of two streams of collisionless particles, circulating in opposite directions with different velocities. We show how such disks can act as exact sources of all types of the Kerr metric. In their central regions they can produce ergoregions, the velocities can approach that of light, and the redshifts can becomes arbitrarily large.