# Bargmann-Wigner Equations, Fermion-Boson Correspondence and Superradiant Problem in Curved Spacetime

## TL;DR

This paper explores the Bargmann-Wigner equations in curved spacetime, revealing fermion-boson correspondence and analyzing superradiance phenomena near rotating black holes, with implications for scattering and stability in Kerr spacetime.

## Contribution

It extends Bargmann-Wigner equations to curved spacetime and demonstrates fermion-boson correspondence, analyzing superradiance in Kerr black holes for the first time.

## Key findings

- Superradiance can occur with negative energy in Kerr spacetime.
- Fermion-boson correspondence is established via Bargmann-Wigner equations.
- Stable superradiant states are possible near black hole horizons.

## Abstract

Bargmann-Wigner equations and their solutions are studied in (3+1)-dimensional curved spacetime. Fermion-Boson correspondence for bi-spinor case is studied through the Bargmann-Wigner equations and solutions over curved spacetime. As an application to scattering phenomena of massive Fermions and Bosons on the rotating black holes, the superradiance with negative energy $(\omega<0)$ and positive effective energy in co-rotating coordinate system near horizon $(\omega-m\Omega_{H}>0)$ is possible to occur as stable physical states in Kerr spacetime.