TL;DR
This paper extends the Ashtekar-Renteln Ansatz to N=1 supergravity, providing both canonical and covariant formulations, and explores geometric properties of the solutions with added insights on wave functions.
Contribution
It introduces a generalization of the Ashtekar-Renteln Ansatz to N=1 supergravity in both formulations, highlighting new geometric features and implications for wave functions.
Findings
Generalization to N=1 supergravity achieved
Geometric properties of solutions identified
Comments on wave function implications included
Abstract
The Ashtekar-Renteln Ansatz gives the self-dual solutions to the Einstein equation. A direct generalization of the Ashtekar-Renteln An\-satz to N=1 supergravity is given both in the canonical and in the covariant formulation and a geometrical property of the solutions is pointed out. (Changes: the covariant formulation and some comments about a wave function has been added)
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