The Generalized Good Cut Equation

Details The Generalized Good Cut Equation The Generalized Good Cut Equation

2010-07-23

arxiv.org/abs/1007.4215v1

Class.Quant.Grav.27:245004,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages

Scientific paper

10.1088/0264-9381/27/24/245004

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.

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