Killing-Yano Forms of a Class of Spherically Symmetric Space-Times I: A Unified Generation of Killing Vector Fields

TL;DR

This paper derives and unifies the Killing-Yano one forms for various spherically symmetric space-times, revealing new forms and symmetries, and providing a comprehensive framework for understanding their Killing vector fields.

Contribution

It introduces a unified method to generate Killing-Yano forms for a broad class of spherically symmetric space-times, including new forms for de Sitter space.

Findings

Derived Killing-Yano forms for well-known space-times.

Identified additional forms of de Sitter space with multiple Killing vectors.

Presented a family of space-times with high symmetry and multiple Killing vectors.

Abstract

Killing-Yano one forms (duals of Killing vector fields) of a class of spherically symmetric space-times characterized by four functions are derived in a unified and exhaustive way. For well-known space-times such as those of Minkowski, Schwarzschild, Reissner-Nordstrom, Robertson-Walker and several forms of de Sitter, these forms arise as special cases in a natural way. Besides its two well-known forms, four more forms of de Sitter space-time are also established with ten independent Killing vector fields for which four different time evolution regimes can explicitly be specified by the symmetry requirement. A family of space-times in which metric characterizing functions are of the general form and admitting six or seven independent Killing vector fields is presented.