The Generalized Good Cut Equation

Abstract

The properties of null geodesic congruences (NGCs) in Lorentzian manifolds are a topic of considerable importance. More specifically NGCs with the special property of being shear-free or asymptotically shear-free (as either infinity or a horizon is approached) have received a great deal of recent attention for a variety of reasons. Such congruences are most easily studied via solutions to what has been referred to as the 'good cut equation' or the 'generalization good cut equation'. It is the purpose of this note to study these equations and show their relationship to each other. In particular we show how they all have a four complex dimensional manifold (known as H-space, or in a special case as complex Minkowski space) as a solution space.

12 pages

References in corpus (5)

• Generic Isolated Horizons and their Applications
• Geometry of Generic Isolated Horizons
• Null Geodesic Congruences, Asymptotically Flat Space-Times and Their Physical Interpretation
• The Universal Cut Function and Type II Metrics
• Vacuum non-expanding horizons and shear-free null geodesic congruences

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• Carrollian manifolds and null infinity: A view from Cartan geometry
• Massless Scalars and Higher-Spin BMS in Any Dimension
• Compact Binary Waveform Center-of-Mass Corrections
• Asymptotic Shear and the Intrinsic Conformal Geometry of Null-Infinity
• Tractor geometry of asymptotically flat spacetimes
• Light cones in relativity: Real, complex and virtual, with applications
• Asymptotic Higher Spin Symmetries III: Noether Realization in Yang-Mills Theory
• Asymptotic Higher Spin Symmetries II: Noether Realization in Gravity
• Asymptotic Higher Spin Symmetries IV: Einstein-Yang-Mills Theory