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Plebanski Formulation of General Relativity: A Practical Introduction

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arxiv 0904.0423 v2 pith:MLGTVWSD submitted 2009-04-02 gr-qc

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keywords formulationplebanskiintroductionalternativecommonlyderivingdescribingdescription
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Graviton scattering on self-dual black holes

    hep-th 2025-07 unverdicted novelty 8.0 of 10

    Exact tree-level MHV graviton scattering amplitudes at arbitrary multiplicity are obtained on self-dual Taub-NUT backgrounds using twistor theory, including spin via Newman-Janis shift, with undeformed celestial symmetries.

  2. Renormalization group flows in area-metric gravity

    gr-qc 2025-07 conditional novelty 7.0 of 10

    The first renormalization group analysis of area-metric gravity shows shape-mismatching masses grow toward the infrared, parity is not emergent, and the Immirzi parameter flow has fixed points at γ=0 and γ=∞.

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