No-go theorem for gravivector and graviscalar on the brane

TL;DR

This paper proves that certain extra-dimensional gravitational modes, specifically gravivector and graviscalar, cannot propagate on the brane in the Randall-Sundrum model, confirming the sufficiency of the RS gauge for brane physics.

Contribution

It establishes a no-go theorem showing that gravivector and graviscalar modes do not have on-shell propagation on the RS brane, clarifying their physical relevance.

Findings

h_{55} has no bulk or brane propagation

h_{5} modes are non-physical

RS gauge is sufficient for brane physics

Abstract

We prove the no-go theorem that the gravivector $(h_{5\mu})$ and graviscalar $(h_{55})$ cannot have any on-shell propagation on the Randall-Sundrum (RS) brane. For this purpose, we analyze all of their linearized equations with the de Donder gauge (5D transverse-tracefree gauge). But we do not introduce any matter source. We use the Z$_2$-symmetry argument and their ($h_{5\mu}, h_{55}$) compatibility conditions with the tensor $h_{\mn}$-equation. It turns out that $h_{55}$ does not have any bulk (massive) and brane (massless) propagations. Although $h_{5\mu}$ has a sort of massive propagations, they do not belong to the physical solution. Hence we confirm that the Randall-Sundrum gauge suffices the on-shell brane physics.