Recovery of the Linearized 4D AdS and dS Schwarzschild Metric in the Karch-Randall Braneworld

TL;DR

This paper analyzes how 4D Schwarzschild metrics in AdS and dS spaces can be recovered from a linearized treatment of the Karch-Randall braneworld model, focusing on graviton modes and static excitations.

Contribution

It provides a linearized framework for deriving 4D Schwarzschild metrics in AdS and dS branes within the Karch-Randall model, including graviton mass and static solutions.

Findings

Reproduced 4D Schwarzschild metrics on the brane.

Determined the graviton mass via elementary methods.

Analyzed static excitations in the braneworld setup.

Abstract

We present a linearized treatment of the Karch-Randall braneworld where an AdS_4 or dS_4 brane is embedded in AdS_5. We examine the quasi-zero graviton mode in detail and reproduce the graviton mass by elementary means for the AdS_5 case. We also determine the axially symmetric, static excitations of the vacuum and demonstrate that they reproduce the 4D AdS_4 and dS_4 Schwarzschild metrics on the brane.