Static axisymmetric spacetimes with non-generic world-line SUSY

TL;DR

This paper investigates the conditions under which static axisymmetric spacetimes admit Killing-Yano tensors related to non-generic world-line supersymmetry, concluding that only the Schwarzschild solution meets these criteria.

Contribution

It characterizes the specific static axisymmetric vacuum solutions that admit Killing-Yano tensors, revealing that Schwarzschild is uniquely compatible under these conditions.

Findings

Only Schwarzschild spacetime admits Killing-Yano tensors in this setting.

Static, axisymmetric, asymptotically flat vacuum solutions with Killing-Yano tensors are exclusive to Schwarzschild.

Provides conditions linking Killing-Yano tensors and non-generic world-line SUSY in vacuum spacetimes.

Abstract

The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of solutions admitting Killing-Yano tensors is considered. In particular, it is shown that static, axisymmetric and asymptotically flat vacuum solutions admitting Killing-Yano tensors are only the Schwarzschild solution.