Constraints on $AdS_5$ Embeddings

TL;DR

This paper demonstrates that embedding certain symmetric branes with spatial curvature into an $AdS_5$ bulk does not produce exponential decay of the geometry away from the brane, impacting brane-localized gravity models.

Contribution

It shows that non-compactified $AdS_5$ embeddings of curved branes do not lead to exponential geometric suppression, challenging assumptions in brane-world gravity theories.

Findings

Embedding does not produce exponential suppression of geometry.

Implications challenge existing brane-localized gravity models.

Results apply to both static and time-dependent maximally symmetric branes.

Abstract

We show that the embedding of either a static or a time dependent maximally 3-symmetric brane with non-zero spatial curvature $k$ into a non-compactified $AdS_5$ bulk does not yield exponential suppression of the geometry away from the brane. Implications of this result for brane-localized gravity are discussed.