Greybody factors of Proca fields in Schwarzschild spacetime: A supplemental analysis based on decoupled master equations related to the Frolov-Krtou\v{s}-Kubiz\v{n}\'ak-Santos separation

TL;DR

This paper analyzes greybody factors for Proca fields in Schwarzschild spacetime, employing decoupled master equations and semi-analytical methods to reveal novel features in transmission probabilities.

Contribution

It introduces a supplemental analysis using decoupled master equations based on a specific transformation, providing new insights into Proca field transmission in black hole backgrounds.

Findings

In the even-parity vector mode, low-mass regimes show higher transmission probabilities than massless cases.

The massless limit of the even-parity scalar mode matches massless scalar perturbation results and is a pure gauge mode.

Massive case transmission probabilities are lower than those of a massive scalar field with same parameters.

Abstract

Greybody factors for Proca fields in Schwarzschild black hole spacetime are investigated. The radial equations are derived by separating the field equations using vector spherical harmonics and decoupling the even-parity sector through Frolov-Krtou\v{s}-Kubiz\v{n}\'ak-Santos transformation in the static limit. Semi-analytical methods, including a rigorous bound and the Wentzel-Kramers-Brillouin approximation, are used to compute the transmission probabilities. In addition to reproducing known results, two distinctive features are identified. In the even-parity vector mode, a low-mass regime is found where the transmission probability exceeds that of the massless case for a set of common energy and angular momentum parameters. In the even-parity scalar mode, the massless limit reproduces the result of massless scalar perturbations and corresponds to a pure gauge mode in Maxwell theory. In the same mode, the transmission probability in the massive case is systematically lower than that of a massive scalar field with the same parameters.