Massive vector field perturbations on extremal and near-extremal static black holes

Understand

We discuss a new perturbation method to study the dynamics of massive vector fields on (near-)extremal static black hole spacetimes.

• We start with, as our background, a rather generic class of warped product metrics, and classify the field variables into the vector(axial)- and scalar(polar)-type components.
• On this generic background, we show that for the vector-type components, the Proca equation reduces to a single master equation, whereas the scalar-type components remain to be coupled.
• Then, focusing on the case of (near-)extremal static black holes in four-dimensions, we consider the near-horizon expansion of both the background geometry and massive vector field by a scaling parameter $\lambda$ with the leading-order geometry being the so called near-horizon geometry.