Integration using invariant operators:Conformally flat radiation metrics

Abstract

A new method is presented for obtaining the general conformally flat radiation metric by using the differential operators of Machado Ramos and Vickers (a generalisation of the GHP operators) which are invariant under null rotations and spin and boosts. The solution is found by constructing involutive tables of these derivatives applied to the quantities which arise in the Karlhede classification of metrics.

23 pages, TeX (uses iopppt.tex)

References in corpus (3)

• Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I
• Integration in the GHP formalism III: Finding all conformally flat radiation metrics as an example of an `optimal situation'
• Integration in the GHP formalism II: An operator approach for spacetimes with killing vectors, with applications to twisting type n spaces

Cited by in corpus (9)

• Explicit algebraic classification of Kundt geometries in any dimension
• Obtaining a class of Type N pure radiation metrics using invariant operators
• On conformally flat and type N pure radiation metrics
• On the Symmetries of the Edgar-Ludwig Metric
• Type O pure radiation metrics with a cosmological constant
• Obtaining a class of Type O pure radiation metrics with a cosmological constant, using invariant operators
• Invariant classification and the generalised invariant formalism: conformally flat pure radiation metrics, with zero cosmological constant
• Invariant classification of vacuum PP-waves
• Symmetry analysis of radiative spacetimes with a null isotropy using GHP formalism