Linearized Modes in Extended and Critical Gravities

TL;DR

This paper constructs explicit linearized modes in extended and critical gravities around AdS spacetimes, analyzing their properties, stability conditions, and boundary behaviors in various dimensions.

Contribution

It provides explicit solutions for linearized modes in extended and critical gravities, including log modes, and analyzes their stability and boundary conditions.

Findings

Modes include massive, massless, vector, scalar, and log modes.

Tachyon-free conditions allow negative mass squared for certain modes.

Some modes can be truncated due to boundary condition issues.

Abstract

We construct explicit solutions for the linearized massive and massless spin-2, vector and scalar modes around the AdS spacetimes in diverse dimensions. These modes may arise in extended (super)gravities with higher curvature terms in general dimensions. Log modes in critical gravities can also be straightforwardly deduced. We analyze the properties of these modes and obtain the tachyon-free condition, which allows negative mass square for these modes. However, such modes may not satisfy the standard AdS boundary condition and can be truncated out from the spectrum.