Surfaces of infinite red-shift around a uniformly accelerating and rotating particle

The structure of the surfaces of infinite red-shift that are formed about an accelerating Kerr-type particle is studied. It is shown that for nonzero acceleration and rotation there exist three relevant surfaces of infinite red-shift. One of these surfaces is analogous to the Schwarzschild surface and is mainly a consequence of the mass. The acceleration causes this surface to expand in the forward direction and contract in the backward direction. In addition, the rotation causes the Schwarzschild surface to contract both in the forward and backward directions. The second surface is mainly due to the acceleration and is called the Rindler surface. It has a shape similar to a parabola of revolution. As the acceleration increases, the Rindler surface moves inward, approaching the Schwarzschild surface. Rotation causes the Rindler surface to contract slightly in the equatorial plane. As the acceleration increases to a critical value the Rindler and the Schwarzschild surfaces coincide on the equatorial plane. As the acceleration is increased further, the points of coincidence spread towards the poles. The third surface is produced mainly by the rotation and is a shape similar to the interior Kerr surface. This surface is called the Kerr surface. By increasing the rotation this surface expands in the polar regions, approaching the Schwarzschild surface. Acceleration causes this surface to distort and become elongated in the forward direction and contracted in the backward direction.