Hidden symmetries of generalised gravitational instantons

Author:

Bernardo Araneda

Keyword:

General Relativity and Quantum Cosmology, General Relativity and Quantum Cosmology (gr-qc), High Energy Physics - Theory (hep-th), Differential Geometry (math.DG)

journal:

date:

2023-09-10 16:00:00

Abstract

For conformally K\"ahler Riemannian four-manifolds with a Killing field, we develop a framework to solve the field equations for generalised gravitational instantons corresponding to conformal self-duality and to cosmological Einstein-Maxwell. We obtain generic identities for the curvature of such manifolds without assuming field equations. After applying the framework to recover standard solutions, we find conformally self-dual generalisations of the Page-Pope, Plebanski-Demianski, and Chen-Teo solutions, which are neither hyper-K\"ahler nor quaternionic-K\"ahler, giving new self-dual gravitational instantons in conformal gravity.

PDF: Hidden symmetries of generalised gravitational instantons.pdf