On conformal Killing-Yano tensors for Plebanski-Demianski family of solutions

TL;DR

This paper derives explicit conformal Killing-Yano tensors for the Plebanski-Demianski family of solutions, explores special cases, and discusses higher-dimensional generalizations, highlighting differences between four and higher dimensions.

Contribution

It provides explicit formulas for conformal Killing-Yano tensors in Plebanski-Demianski solutions and analyzes their behavior in special cases and higher dimensions.

Findings

Conformal Killing-Yano tensors reduce to Killing-Yano tensors in non-accelerating solutions.

Higher-dimensional generalizations are limited to maximally symmetric spacetimes.

Transition from accelerating to non-accelerating solutions involves conformal rescaling in four dimensions.

Abstract

We present the explicit expressions for the conformal Killing-Yano tensors for the Plebanski-Demianski family of type D solutions in four dimensions. Some physically important special cases are discussed in more detail. In particular, it is demonstrated how the conformal Killing-Yano tensor becomes the Killing-Yano tensor for the solutions without acceleration. A possible generalization into higher dimensions is studied. Whereas the transition from the nonaccelerating to accelerating solutions in four dimensions is achieved by the conformal rescaling of the metric, we show that such a procedure is not sufficiently general in higher dimensions - only the maximally symmetric spacetimes in 'accelerated' coordinates are obtained.