A Radiating and Rotating Metric

TL;DR

This paper derives a new non-static, axisymmetric solution to Einstein's field equations that generalizes the Kerr metric by allowing the mass parameter to vary with null-time, unifying Kerr and Vaidya solutions.

Contribution

It introduces a novel metric that extends the Kerr solution to include radiating, axisymmetric gravitational fields with a variable mass parameter.

Findings

The solution reduces to the Kerr metric when mass is constant.

It simplifies to the Vaidya metric when angular momentum is zero.

The metric describes a radiating, rotating gravitational field.

Abstract

A non-static solution of Einstein's field equations of General Relativity representing the gravitational field of an axisymmetric radiation flow is obtained using the Eddington or the Kerr-Schild form for the metric. A solution obtained here manifestly corresponds to the Kerr metric with its mass-parameter, $m$, being an arbitrary function of the advanced (retarded) null-time coordinate. Then, when $m$ is constant, the solution reduces to the standard Kerr metric expressed in terms of the used null coordinate. Further, when the angular momentum parameter, $a$, a constant here, is set to zero, the solution reduces to the Vaidya metric expressed in terms of the used null-coordinate.