Gray-body factors: Method matters

TL;DR

This paper compares two methods for calculating gray-body factors in rotating black holes, revealing that the traditional Chandrasekhar approach overestimates values in the superradiant regime, impacting astrophysical constraints.

Contribution

It introduces an alternative computational method for gray-body factors in Kerr black holes and demonstrates its improved accuracy over Chandrasekhar's formalism.

Findings

Chandrasekhar method overestimates gray-body factors in superradiant regime.

For near-maximal spin, Chandrasekhar yields twice the correct value.

Discrepancies affect constraints from gamma-ray observations.

Abstract

The calculation of gray-body factors is essential for understanding Hawking radiation and black hole thermodynamics. While the formalism developed by Chandrasekhar is effective for static black holes, it faces significant challenges in Kerr spacetimes, particularly in the superradiant regime, where a specific choice of coordinates introduces numerical inaccuracies. To address these limitations, an alternative method based on re-scaling radial coordinates and employing Frobenius-like expansions has been investigated. We compare the gray-body factors obtained for a near-maximally rotating black hole using both methods and find that the Chandrasekhar formalism systematically overestimates the values in the superradiant regime compared to well-established analytical results. Specifically, for a spin parameter of $a_* = 0.999$, the Chandrasekhar method yields values approximately twice as large as the correct result. Since this approach has been implemented in \texttt{BlackHawk}, we assess the impact of these discrepancies on constraints derived from gamma-ray observations of highly spinning primordial black holes.