Warped-brane proper acceleration
= Warped-brane proper acceleration
{title2=$|a|=1/L$}
An inertial observer of a fixed-$y$ flat brane in metric $dy^2+e^{-2y/L}\eta_{\mu\nu}dx^\mu dx^\nu$ is accelerated relative to the higher-dimensional bulk. Normalization and $\Gamma^y_{\mu\nu}=e^{-2y/L}\eta_{\mu\nu}/L$ give $a^y=-1/L$. This is its invariant bulk <proper acceleration>, not a nonzero intrinsic four-dimensional acceleration on the flat induced brane metric.