Isometric invariance of the positive-frequency kernel in generalized FRW-like spacetimes

TL;DR

This paper investigates the invariance properties of the positive-frequency kernel in Klein-Gordon equations within generalized FRW-like spacetimes, showing that the kernel remains invariant under continuous isometries except in special cases.

Contribution

It extends the understanding of isometric invariance of the positive-frequency kernel to more general FRW-like spacetimes with compact, non-isotropic, and non-homogeneous spatial sections.

Findings

Kernel is invariant under continuous isometries in most cases.

Exceptional cases where invariance does not hold are identified.

Results generalize previous invariance findings to broader spacetime classes.

Abstract

Klein-Gordon equation with minimal coupling in FRW-like spacetimes with compact but not necessarily isotropic neither homogeneous space sections. Beside exceptional cases, the kernel is invariant under continuous isometries.