Hidden Conformal Symmetry for Vector Field on Various Black Hole Backgrounds

TL;DR

This paper demonstrates that hidden conformal symmetry, previously studied for scalar fields, also appears for vector fields in various black hole backgrounds under near-region and low-frequency conditions.

Contribution

It extends the analysis of hidden conformal symmetry to vector fields on Kerr-(A)dS and Kerr-NUT-(A)dS black holes, using separation of variables for Maxwell equations.

Findings

Hidden conformal symmetry appears for vector fields in near-horizon, low-frequency limits.

The results generalize previous scalar field findings to vector fields.

Symmetry is observed across multiple black hole backgrounds.

Abstract

Hidden conformal symmetries of scalar field on various black hole backgrounds have been investigated for years, but whether those features holds for other fields are still open questions. Recently, with proper assumptions, Lunin achieves to the separation of variables for Maxwell equations on Kerr background. In this paper, with that equation, we find that hidden conformal symmetry appears at near region under low frequency limit. We also extended those results to vector field on Kerr-(A)dS and Kerr-NUT-(A)dS backgrounds, then hidden conformal symmetry also appears if we focusing on the near-horizon region at low frequency limit.