# Massive tensor field perturbations on extremal and near-extremal static black holes

## TL;DR

This paper introduces a new perturbation method to analyze the dynamics of massive tensor fields around extremal and near-extremal static black holes in arbitrary dimensions, simplifying the equations into decoupled wave equations.

## Contribution

The authors develop a novel perturbation approach that reduces complex coupled equations into decoupled wave equations for massive tensor fields on extremal black hole backgrounds.

## Key findings

- Derivation of a master equation for tensor-type components.
- Decoupling of vector and scalar-type components into five wave equations.
- Applicable to arbitrary dimensions and near-horizon geometries.

## Abstract

We develop a new perturbation method to study the dynamics of massive tensor fields on extremal and near-extremal static black hole spacetimes in arbitrary dimensions. On such backgrounds, one can classify the components of massive tensor fields into the tensor, vector, and scalar-type components. For the tensor-type components, which arise only in higher dimensions, the massive tensor field equation reduces to a single master equation, whereas the vector and scalar-type components remain coupled. We consider the near-horizon expansion of both the geometry and the field variables with respect to the near-horizon scaling parameter. By doing so, we reduce, at each order of the expansion, the equations of motion for the vector and scalar-type components to a set of five mutually decoupled wave equations with source terms consisting only of the lower-order variables. Thus, together with the tensor-type master equation, we obtain the set of mutually decoupled equations at each order of the expansion that govern all dynamical degrees of freedom of the massive tensor field on the extremal and near-extremal static black hole background.