On local equivalence problem of spacetimes with two orthogonally transitive commuting Killing fields

TL;DR

This paper addresses the local equivalence problem for four-dimensional spacetimes with two orthogonally transitive commuting Killing fields, constructing explicit differential invariants to classify such metrics.

Contribution

The authors explicitly construct a set of eight differential invariants for classifying these spacetimes, with a simplified set sufficing in the vacuum case.

Findings

Eight differential invariants explicitly constructed

Four first-order invariants suffice in vacuum case

Method aids in classifying spacetimes with symmetries

Abstract

Considered is the problem of local equivalence of generic four-dimensional metrics possessing two commuting and orthogonally transitive Killing vector fields. A sufficient set of eight differential invariants is explicitly constructed, among them four of first order and four of second order in terms of metric coefficients. In vacuum case the four first-order invariants suffice to distinguish generic metrics.