Some metrics admitting nonpolynomial first integrals of the geodesic equation

TL;DR

This paper constructs metrics with nonpolynomial first integrals of the geodesic equation, revealing a chain of generalized Killing vectors, thus expanding the understanding of integrals beyond polynomial cases.

Contribution

It introduces new metrics that admit nonpolynomial first integrals, demonstrating a novel class of solutions linked to generalized Killing vectors.

Findings

Metrics with nonpolynomial first integrals are explicitly constructed.

These metrics reveal a chain of generalized Killing vectors.

The work broadens the class of known integrals of the geodesic equation.

Abstract

It is commonly known that Killing vectors and tensors are in one-to-one correspondence with polynomial first integrals of the geodesic equation. In this work, metrics admitting nonpolynomial first integrals of the geodesic equation are constructed, each of which revealing a chain of generalised Killing vectors.