Massive vector fields in Kerr--Newman and Kerr--Sen black hole spacetimes

TL;DR

This paper investigates superradiant instability modes of ultralight massive vector bosons around rotating black holes in Einstein--Maxwell and heterotic string theories, revealing separability of equations and identifying the most unstable modes.

Contribution

It demonstrates the full separability of Proca equations in Kerr--Newman and Kerr--Sen spacetimes and numerically analyzes the most unstable superradiant modes.

Findings

Proca equations are fully separable in both backgrounds.

Numerical solutions identify the most unstable superradiant modes.

Comparison shows differences from the Kerr black hole case.

Abstract

The superradiant instability modes of ultralight massive vector bosons are studied for weakly charged rotating black holes in Einstein--Maxwell gravity (the Kerr--Newman solution) and low-energy heterotic string theory (the Kerr--Sen black hole). We show that in both these cases, the corresponding massive vector (Proca) equations can be fully separated, exploiting the hidden symmetry present in these spacetimes. The resultant ordinary differential equations are solved numerically to find the most unstable modes of the Proca field in the two backgrounds and compared to the vacuum (Kerr black hole) case.