Relativistic Rotational Darkening of Lightlike Radiation and Von Zeipel's Theorem for Radially Emitting Spheroids

Abstract

It is shown that an outgoing null radiation field in the outer space of a Kerr-Newman black hole is darkened by the rotation of the black hole. This rotational darkening is calculated for a spheroid emitting null radiation normally to its surface, yielding the von Zeipel-like effectthat the equatorial region is darkened more strongly than the polar regions.This effect is not confined to the case of black holes but is also observable for relativistically rotating fluid spheroids such as atmospheres of pulsars or neutron stars. Moreover, application to Hawking radiation suggests that the black hole cannot be viewed as a classical black body but that the Hawking radiationis a global geometric effect.