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1997•Journal of Mathematical PhysicsRequires access

A Lanczos potential in Kerr geometry

Göran Bergqvist

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Abstract

A Lanczos potential is a tensor of rank 3 for which a certain combination of derivatives always equals the Weyl tensor. General existence theorems have been proved before and some explicit expressions for Lanczos potentials in certain spacetimes have been found. In this paper we explicitly study a Lanczos potential in Kerr spacetime obtained from a previously studied flat connection. As an application it is shown that the mass can be expressed as an integral of the Lanczos potential.

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What this paper is about

A Lanczos potential is a tensor of rank 3 for which a certain combination of derivatives always equals the Weyl tensor. General existence theorems have been proved before and some explicit expressions for Lanczos potentials in certain spacetimes have been found. In this paper we explicitly study a Lanczos potential in Kerr spacetime obtained from a previously studied flat connection. As an application it is shown that the mass can be expressed as an integral of the Lanczos potential.

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Available abstract

A Lanczos potential is a tensor of rank 3 for which a certain combination of derivatives always equals the Weyl tensor. General existence theorems have been proved before and some explicit expressions for Lanczos potentials in certain spacetimes have been found. In this paper we explicitly study a Lanczos potential in Kerr spacetime obtained from a previously studied flat connection. As an application it is shown that the mass can be expressed as an integral of the Lanczos potential.

Key concepts: Lanczos tensor, Lanczos resampling, Spacetime, Lanczos algorithm, Mathematical physics, Rank (graph theory), Tensor (intrinsic definition), Connection (principal bundle)

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