Gravitational Instantons in Ashtekar's Formalism

TL;DR

This paper constructs gravitational instantons of Bianchi type IX in Ashtekar's formalism by solving all constraints and Hamiltonian equations, applicable to matter-coupled systems with a cosmological constant.

Contribution

It provides a complete solution to gravitational instantons in Ashtekar's formalism without relying on self-duality, extending applicability to matter and cosmological constant.

Findings

Explicit construction of Bianchi type IX instantons

Solution of all constraints and Hamiltonian equations

Applicability to matter-coupled systems with cosmological constant

Abstract

Gravitational instantons of Bianchi type IX space are constructed in Ashtekar's canonical formalism. Instead of solving the self-duality condition, we fully solve the constraint on the ``initial surface'' and ``Hamiltonian equations''. This formalism is applicable to the matter coupled system with cosmological constant.