A power law for the lowest eigenvalue in localized massive gravity

TL;DR

This paper analyzes the eigenvalue behavior of a localized massive graviton in a 4D AdS background, revealing a quadratic dependence on the cosmological constant, contrasting previous linear assumptions.

Contribution

It provides a detailed derivation of the power law for the lowest eigenvalue, showing it follows a quadratic relation with the cosmological constant.

Findings

Lowest eigenvalue follows a quadratic power law

Contrasts previous linear dependence assumptions

Enhances understanding of massive gravity in AdS backgrounds

Abstract

This short note contains a detailed analysis to find the right power law the lowest eigenvalue of a localized massive graviton bound state in a four dimensional AdS background has to satisfy. In contrast to a linear dependence of the cosmological constant we find a quadratic one [hep-th/0011156].