Phantom Metrics With Killing Spinors

TL;DR

This paper explores special metric solutions in Einstein-anti-Maxwell theory that admit Killing spinors, including space-like Killing vector solutions, Kasner spaces, and Euclidean solutions, expanding understanding of supersymmetric geometries.

Contribution

It introduces an analogue of the IWP metric with space-like Killing vectors and constructs explicit electric, magnetic, and Euclidean solutions within this framework.

Findings

Derived a new class of metrics with Killing spinors in Einstein-anti-Maxwell theory.

Constructed explicit Kasner space solutions with time-dependent metrics.

Presented Euclidean solutions extending the class of known supersymmetric geometries.

Abstract

We study metric solutions of Einstein-anti-Maxwell theory admitting Killing spinors. The analogue of the IWP metric which admits a space-like Killing vector is found and is expressed in terms of a complex function satisfying the wave equation in flat (2+1)-dimensional space-time. As examples, electric and magnetic Kasner spaces are constructed by allowing the solution to depend only on the time coordinate. Euclidean solutions are also presented.