f-symbols, Killing tensors and conserved Bel-type currents

TL;DR

This paper explores how generalized Killing vector fields in General Relativity can be used to construct conserved currents by contracting them with Bel-type tensors, enhancing understanding of conserved quantities in Einstein spaces.

Contribution

It introduces a method to derive conserved currents from f-symbols, Stäckel-Killing, and Killing-Yano tensors contracted with Bel or Bel-Robinson tensors in Einstein spaces, extending previous work.

Findings

Conserved currents can be constructed from generalized Killing tensors and Bel-type tensors.

The approach applies specifically to Einstein spaces.

Provides a new perspective on conserved quantities in General Relativity.

Abstract

In the framework of the General Relativity we show that from three generalizations of Killing vector fields, namely f-symbols, symmetric St\"{a}ckel-Killing and antisymmetric Killing-Yano tensors, some conserved currents can be obtained through adequate contractions of the above mentioned objects with rank four tensors having the properties of Bel or Bel-Robinson tensors in Einstein spaces.