Gravitation without black holes.

TLDR: In this article, the authors consider the singularity problem in deriving the metric external to a static spherically symmetric body of mass qn, which is the Schwarzschild curvature singularity.

Abstract: In recent years much work has been devoted to the development of the (i singularity theorems ~ of Hawking and Penrose in order to have a bet ter understanding of the properties of space-times in Einstein 's general theory of re la t iv i ty (1). In spite, however, of the significant advances made in the subject, many impor tant problems of the classical theory of singularities remain still unsolved. The results obtained t i l l now, support the feeling tha t physically realistic solutions to the Einstein 's equations that are singulari ty free can only be obtained either by modifying the field equations or by looking for some missing physics in the applied general relat ivi ty. To be more concrete, let us consider the singulari ty which occurs in deriving the metric external to a static spherically symmetr ic body of mass qn, tha t is the Schwarzschild curvature singularity. This is a part icularly simple situation so, assuming the val id i ty of Einstein 's equations of general relativity, we can t ry to look for a minimal physical ansatz which can lead to singularity-free solutions. The most obvious suggestion might be to explore which physical proper ty one could at t r ibute to the body, besides its mass m, in order to get a well-behaved line element. Otherwise stated, between the many parameter familes of asymptot ical ly flat solutions which generalize che Schwarzschild case, one should succeed in choosing a suitable set of parameter to which correspond regular solutions. In stat ionary nonspherieal situations, however, i t is known tha t the Kerr-Newman solutions, where the parameters are the mass m, the electric charge q, the magneticmonopole charge p and a rotation parameter a, still display horizons, naked singularities and other unwanted phenomena. The simplest generalization of the Schwarzsehild problem, in which to the mass m is associated a scalar charge a, does not seem to have been adequately t reated in the li terature.