Physical properties of a source of the Kerr metric: Bound on the surface gravitational potential and conditions for the fragmentation

TL;DR

This paper analyzes the physical limits of a Kerr metric interior solution, identifying a maximum surface potential to avoid anomalies and exploring conditions under which the source may fragment, differing from spherical cases.

Contribution

It introduces a bound on the surface gravitational potential for Kerr sources and examines fragmentation conditions, extending previous spherical models to rotating bodies.

Findings

Existence of a maximum surface potential for Kerr sources.

Negative gravitational acceleration linked to pressure anomalies.

Differences in fragmentation scenarios compared to spherical models.

Abstract

We investigate some important physical aspects of a recently presented interior solution for the Kerr metric. It is shown that, as in the spherically symmetric case, there is a specific limit for the maximal value of the surface potential (degree of compactness), beyond which, unacceptable physical anomalies appear. Such a bound is related to the appearance of negative (repulsive) gravitational acceleration, that is accompanied by the appearance of negative values of the pressure. A detailed discussion on this effect is presented. We also study the possibility of a fragmentation scenario, assuming that the source leaves the equilibrium, and we bring out the differences with the spherically symmetric case.