Dynamical vs. Auxiliary Fields in Gravitational Waves around a Black Hole

TL;DR

This paper applies an auxiliary/dynamic decoupling method to analyze gravitational perturbations around higher-dimensional Schwarzschild black holes, simplifying computations and providing new insights into master equations without complex gauge fixing.

Contribution

It extends the auxiliary/dynamic decoupling method to higher-dimensional black holes, offering a straightforward approach that aligns with previous results but avoids complex variable definitions.

Findings

Reproduces known perturbation results for Schwarzschild black holes.

Simplifies the derivation of master equations without gauge fixing.

Provides a canonical conjugate relationship between emergent master fields.

Abstract

The auxiliary/dynamic decoupling method of hep-th/0609001 applies to perturbations of any co-homogeneity 1 background (such as a spherically symmetric space-time or a homogeneous cosmology). Here it is applied to compute the perturbations around a Schwarzschild black hole in an arbitrary dimension. The method provides a clear insight for the existence of master equations. The computation is straightforward, coincides with previous results of Regge-Wheeler, Zerilli and Kodama-Ishibashi but does not require any ingenuity in either the definition of variables or in fixing the gauge. We note that the method's emergent master fields are canonically conjugate to the standard ones. In addition, our action approach yields the auxiliary sectors.