A formalism for analyzing vacuum spacetimes
Michael Reiterer (ETH Zurich), Eugene Trubowitz (ETH Zurich)
TL;DR
This paper introduces a new formalism for analyzing vacuum spacetimes using Lie superbrackets, providing clearer covariance properties and aiding in the analytic study of Einstein vacuum equations.
Contribution
It develops a formalism expressing Einstein vacuum equations via Lie superbrackets, enhancing understanding of their covariance and analytical properties.
Findings
Formalism clarifies covariance properties of vacuum equations
Differential identities derived from super Jacobi identity
Framework aids in analytic studies of vacuum spacetimes
Abstract
The Einstein vacuum equations in the formulation developed by Newman, Penrose [NP] and Friedrich [Fr] are expressed in terms of a Lie superbracket. Differential identities are derived from the super Jacobi identity. This perspective clarifies the covariance properties of the equations. The equations are intended as a tool for the analytic study of vacuum spacetimes.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Noncommutative and Quantum Gravity Theories · Geophysics and Sensor Technology