Linearized Einstein theory via null surfaces

Details Linearized Einstein theory via null surfaces Linearized Einstein theory via null surfaces

1995-02-10

arxiv.org/abs/gr-qc/9502026v1

J.Math.Phys. 36 (1995) 5005-5022

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages

Scientific paper

10.1063/1.531211

Recently there has been developed a reformulation of General Relativity - referred to as {\it the null surface version of GR} - where instead of the metric field as the basic variable of the theory, families of three-surfaces in a four-manifold become basic. From these surfaces themselves, a conformal metric, conformal to an Einstein metric, can be constructed. A choice of conformal factor turns them into Einstein metrics. The surfaces are then automatically characteristic surfaces of this metric. In the present paper we explore the linearization of this {\it null surface theory} and compare it with the standard linear GR. This allows a better understanding of many of the subtle mathematical issues and sheds light on some of the obscure points of the null surface theory. It furthermore permits a very simple solution generating scheme for the linear theory and the beginning of a perturbation scheme for the full theory.

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