A semi-tetrad decomposition of the Kerr spacetime

TL;DR

This paper introduces a novel semi-tetrad 1+1+2 covariant formalism for analyzing Kerr spacetime, providing explicit quantities and equations that enhance geometric understanding and correct previous formalism errors.

Contribution

The paper applies the 1+1+2 covariant method to Kerr spacetime, offering new explicit geometric quantities and correcting earlier formalism equations.

Findings

Explicit 1+1+2 Kerr quantities derived

Evolution and propagation equations formulated

Corrections made to previous formalism equations

Abstract

In this paper we perform a semi-tetrad decomposition of the Kerr spacetime. We apply the 1+1+2 covariant method to the Kerr spacetime in order to describe its geometry outside the ergoregion. As a result we are able to explicitly write down the 1+1+2 Kerr quantities, and the evolution and propagation equations they satisfy. This formalism allows us to present the kinematic and dynamic quantities in a transparent geometrical manner; and also to highlight the role of vorticity. To our knowledge, using the 1+1+2 formalism to investigate the Kerr spacetime is a novel approach and this provides new insights into the spacetime geometry in an easier manner than alternate approaches. Furthermore we make corrections to earlier equations in the 1+1+2 formalism applied to the Kerr spacetime.