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ale space

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46 - Vielbein-Spin Connection Formulation of General Relativity and Gravitational Instantons
from Part III - Other Spins or Statistics; General Relativity
Horaƫiu Năstase, Universidade Estadual Paulista, São Paulo
Book:

Classical Field Theory

Published online:

04 March 2019

Print publication:

14 March 2019, pp 441-454
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Summary

We start by defining the vielbein-spin connection formulation of general relativity and the Palatini formalism. Next we define the Taub–NUT solutions and their analytical continuation, the Euclidean gravitational instanton defined by Hawking. Next, following the example of the Yang–Mills instanton, we write the Einstein equations in Euclidean signature as self-duality equations for the spin connection, which we solve by an instanton ansatz, obtaining the Eguchi–Hanson metric, and example of ALE space. We rewrite it and generalize it in the form of the Gibbons–Hawking multi-instanton solution.