Plebanski Formulation of General Relativity: A Practical Introduction

Details Plebanski Formulation of General Relativity: A Practical Introduction Plebanski Formulation of General Relativity: A Practical Introduction

2009-04-02

arxiv.org/abs/0904.0423v2

Gen.Rel.Grav.43:1-15,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

(v1) 13 pages, no figures (v2) 15 pages, published version

Scientific paper

10.1007/s10714-010-1061-x

We give a pedagogical introduction into an old, but unfortunately not commonly known formulation of GR in terms of self-dual two-forms due to in particular Jerzy Plebanski. Our presentation is rather explicit in that we show how the familiar textbook solutions: Schwarzschild, Volkoff-Oppenheimer, as well as those describing the Newtonian limit, a gravitational wave and the homogeneous isotropic Universe can be obtained within this formalism. Our description shows how Plebanski formulation gives quite an economical alternative to the usual metric and frame-based schemes for deriving Einstein equations.

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