No Van Dam-Veltman-Zakharov Discontinuity in Ads Space

TL;DR

This paper demonstrates that the van Dam-Veltman-Zakharov discontinuity, problematic in Minkowski space, does not occur in Anti De Sitter space, indicating a smooth massless limit under certain conditions.

Contribution

It proves the absence of the VDVZ discontinuity in AdS space and clarifies conditions for a smooth massless limit in massive gravity theories.

Findings

VDVZ discontinuity is specific to Minkowski space

No discontinuity in AdS space for the massless limit

Smooth massless limit when graviton mass squared vanishes faster than cosmological constant

Abstract

We prove that the van Dam-Veltman-Zakharov discontinuity arising in the massless limit of massive gravity theories is peculiar to Minkowski space and it is not present in Anti De Sitter space, where the massless limit is smooth. More generally, the massless limit is smooth whenever the square of the graviton mass vanishes faster than the cosmological constant.