Mass Formula for a Stationary Axisymmetric Configuration and the Physical Realization of the Kerr Metric

TL;DR

This paper examines the mass formula for stationary axisymmetric systems in general relativity and argues that real matter configurations cannot produce the Kerr metric as a stationary equilibrium solution.

Contribution

It provides a new analysis of the mass formula and demonstrates the incompatibility of real matter distributions with the Kerr metric in stationary equilibrium.

Findings

Mass formula analyzed for axisymmetric configurations.

Incompatibility shown between real matter sources and Kerr metric.

Stationary equilibrium of real matter cannot generate Kerr spacetime.

Abstract

We analyse the expression for the mass of a stationary axisymmetric configuration in general relativity obtained in our previous work [1]. From the generality of our formula and its incompatibility with the corresponding expression in Kerr space-time we argue that a stationary equilibrium distribution of a real matter cannot be a source of the Kerr metric.