Perturbations of an Arbitrary Spherically Symmetric Metric

Abstract

RECENT discoveries of unusual astrophysical objects, such as pulsars and quasars, have given renewed impetus to the development of general relativistic astrophysics, of which a survey is found in ref. 1. In particular, the gravitational collapse of massive bodies has been extensively studied in the past few years². Most of this work has been done under the simplifying assumption of spherical symmetry. This assumption negates the possibility of studying such topics as the influence of rotation upon the rate of collapse and gravitational radiation during collapse. Some studies of these topics have been undertaken for very special types of perturbation of spherical symmetry³. On the other hand, a good beginning has been made in the study of arbitrary first-order perturbations around static spherically symmetric equilibrium states⁴.