Revisiting the fermionic quasi-bound states around Schwarzschild black holes with improved analytic spectrum

TL;DR

This paper introduces an improved analytical method for studying fermionic quasi-bound states around Schwarzschild black holes, providing more accurate energy spectra by incorporating high-order angular corrections.

Contribution

It develops a novel matching scheme for the Dirac equation, enabling analytical solutions and improved spectral accuracy over previous second-order approaches.

Findings

Analytical spectrum aligns better with numerical results.

High-order angular corrections significantly improve accuracy.

Method simplifies analysis of fermionic fields near black holes.

Abstract

Black holes have long served as a testing ground for probing theories of gravity and quantum mechanics. Notably, fundamental fields in the neighborhood of black holes exhibit rich phenomena that could yield astrophysical observable signatures. However, exploring these structures typically requires computationally intensive numerical calculations. In this work, the dynamics of a massive Dirac field outside a Schwarzschild black hole is revisited. We propose a novel matching scheme that enables the analytical solution of the coupled first-order Dirac equation, as opposed to the conventional second-order approach. This method yields a compact and unified analytical expression for the energy spectrum, which shows improved agreement with numerical results. The improvement is due to high-order correction of angular parameter that has been ignored previously.