Gravitational waves originated before compactification in Kaluza-Klein theory

TL;DR

This paper explores how gravitational waves generated before compactification in higher dimensions influence observable 4D gravitational and gauge fields, considering internal space curvature effects and conditions for static internal spaces.

Contribution

It extends previous work by analyzing gravitational wave propagation with an n-sphere internal space and derives 4D harmonic gauge conditions, highlighting the impact of internal space curvature.

Findings

Internal space curvature prevents static internal space without cosmological constant.

Propagation effects of multidimensional waves are explicitly shown in 4D spacetime.

Presence of cosmological constant allows static internal space, similar to one-dimensional case.

Abstract

We investigate the propagation of multidimensional gravitational waves generated before compactification and observes today as 4-dimensional gravitational waves and gauge fields by generalizing the investigation of Alesci and Montani(AM) to the case where the internal space is an n-sphere. We also derive the 4-dimensional forms of the multidimensional harmonic gauge condition. The primary difference from the case of AM comes from the effect of curvature of the internal space which prevent the space to be static. The other effects are explicitly shown for propagation of the waves in our 4-dimensional spacetime. Static internal space exists if multidimensional cosmologicalconstant is present. Then the situation is similar to the one-dimensional internal space.