A gauge theoretic approach to Einstein 4-manifolds

Abstract

This article investigates a new gauge theoretic approach to Einstein's equations in dimension 4. Whilst aspects of the formalism are already explained in various places in the mathematics and physics literature, our first goal is to give a single coherent account of the theory in purely mathematical language. We then explain why the new approach may have important mathematical applications: the possibility of using the calculus of variations to find Einstein 4-manifolds, as well as links to symplectic topology. We also carry out some of the technical groundwork to attack these problems.

v1: 23 pages, plus references. v2: reference added to article of Richard-Seshadri, typos corrected. v3 putting published version on arxiv

References in corpus (2)

• New Action Principle for General Relativity
• Positive isotropic curvature and self-duality in dimension 4

Cited by in corpus (6)

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• Pure Connection Formulation, Twistors and the Chase for a Twistor Action for General Relativity
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• Gravitons and a complex of differential operators
• A 4D gravity theory and G2-holonomy manifolds