# Quasinormal modes of $p$-forms in spherical black holes

## TL;DR

This paper analyzes the quasinormal modes of p-form fields in spherical black holes across various dimensions, demonstrating stability and providing explicit calculations of mode frequencies using advanced mathematical techniques.

## Contribution

It introduces a method to express p-form fields in terms of coexact forms, derives master equations, and computes quasinormal modes in dimensions up to 10, establishing stability.

## Key findings

- Proves stability of p-form fields in spherical black holes.
- Calculates quasinormal mode frequencies for p-forms in D≤10 dimensions.
- Provides a new framework for analyzing p-form perturbations in black hole spacetimes.

## Abstract

We study the quasinormal modes of $p$-form fields in spherical black holes in $D$-dimensions. Using the spherical symmetry of the black holes and gauge symmetry, we show the $p$-form field can be expressed in terms of the coexact $p$-form and the coexact $(p-1)$-form on the sphere $S^{D-2}$. These variables allow us to find the master equations. By utilizing the S-deformation method, we explicitly show the stability of $p$-form fields in the spherical black hole spacetime. Moreover, using the WKB approximation, we calculate the quasinormal modes of the $p$-form fields in $D(\leq10)$-dimensions.