Killing tensors in foliated spacetimes and photon surfaces

TL;DR

This paper presents a geometric method for constructing nontrivial Killing tensors in foliated spacetimes, linking them to photon surfaces, and demonstrates its application by finding a new Killing tensor in a specific gravity model.

Contribution

It introduces a novel geometric approach to generate Killing tensors in foliated spacetimes and applies it to discover a previously unknown Killing tensor in dilaton-axion gravity.

Findings

Constructed a new Killing tensor for Nutty dyon in dilaton-axion gravity.

Linked Killing tensors to generalized photon surfaces in foliated spacetimes.

Validated the method on known cases.

Abstract

We discuss a recently proposed geometric method for constructing a nontrivial Killing tensor of rank two in a foliated spacetime of codimension one that lifts trivial Killing tensors from slices to the entire manifold. The existence of nontrivial Killing tensor is closely related to generalized photon surfaces. The method is illustrated in some known cases and used to construct the hitherto unknown Killing tensor for the Nutty dyon in dilaton-axion gravity.