Killing-Yano Forms of a Class of Spherically Symmetric Space-Times II: A Unified Generation of Higher Forms

TL;DR

This paper systematically derives Killing-Yano forms for a broad class of spherically symmetric space-times, revealing their structure and limitations, including Minkowski, Schwarzschild, Reissner-Nordstrom, Robertson-Walker, and de Sitter spaces.

Contribution

It provides a unified and exhaustive method to generate and list higher-order Killing-Yano forms for various spherically symmetric space-times, clarifying their existence and properties.

Findings

Schwarzschild and Reissner-Nordstrom do not admit KY 3-forms.

Robertson-Walker admits four KY 2-forms and one KY 3-form.

Minkowski and de Sitter spaces have the maximal number of KY-forms.

Abstract

Killing-Yano (KY) two and three forms of a class of spherically symmetric space-times that includes the well-known Minkowski, Schwarzschild, Reissner-Nordstrom, Robertson-Walker and six different forms of de Sitter space-times as special cases are derived in a unified and exhaustive manner. It is directly proved that while the Schwarzschild and Reissner-Nordstrom space-times do not accept any KY 3-form and they accept only one 2-form, the Robertson-Walker space-time admits four KY 2-forms and only one KY 3-form. Maximal number of KY-forms are obtained for Minkowski and all known forms of de Sitter space-times. Complete lists comprising explicit expressions of KY-forms are given.