nLab Plebanski formulation of gravity

Contents

Formalism

Definition

Spacetime configurations

Properties

Spacetimes

black hole spacetimes	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild spacetime	Kerr spacetime
positive charge	Reissner-Nordstrom spacetime	Kerr-Newman spacetime

black hole spacetimes with dark energy	vanishing angular momentum	positive angular momentum
vanishing charge	Schwarzschild-de Sitter spacetime	Kerr-de Sitter spacetime
positive charge	Reissner-Nordström-de Sitter spacetime	Kerr-Newman-de Sitter spacetime

wormhole spacetimes	vanishing angular momentum
vanishing charge	Schwarzschild wormhole
positive charge	Reissner-Nordström wormhole

Quantum theory

Idea

A certain formulation of the theory of gravity.

The original article is

Plebanski, On the separation of Einsteinian substructures, J. Math. Phys. 18, 2511 (1977) (doi)

An account of the general formalism is in

R. Capovilla, T. Jacobson, J. Dell, L. Mason, Selfdual 2-forms and gravity Classical and Quantum Gravity 8, 41 (1991) (doi).

On practical computations:

Kirill Krasnov, Plebanski Formulation of General Relativity: A Practical Introduction (arXiv)

Boris Kruglikov, Oleg Morozov: $SDiff(2)$ and uniqueness of the Plebański equation, J. Math. Phys. 53 083506 (2012) [doi:10.1063/1.4739749, arXiv:1204.3577v2]

Last revised on January 17, 2026 at 16:30:21. See the history of this page for a list of all contributions to it.