Convergence of Higher-Curvature Expansions Near the Horizon: Hawking Radiation from Regular Black Holes

TL;DR

This paper investigates how higher-curvature series expansions converge near black hole horizons, revealing that while some observables converge quickly, Hawking radiation calculations require many terms for accuracy.

Contribution

The study analyzes the convergence behavior of higher-curvature expansions near black hole horizons, especially for Hawking radiation, highlighting the need for multiple terms for precise results.

Findings

Series converges rapidly for geometry near potential peak

Hawking radiation calculations require many expansion terms

Regular black hole solutions are approached in the infinite limit

Abstract

A recently proposed model incorporating a series of higher-curvature corrections allows for analytic black-hole solutions at each order of the expansion, with a fully regular black hole emerging in the limit of infinite number of terms. An important question that arises within this framework is how rapidly the series converges. For those classical observables, which are primarily determined by the geometry near the peak of the effective potential, it has been previously shown that the series converges remarkably fast, often within the first two orders. However, this rapid convergence does not extend to quantities such as Hawking radiation, which are highly sensitive to the geometry near the event horizon. Although each successive order yields a result that is significantly closer to that of the full infinite series, several terms are typically required to obtain a sufficiently accurate approximation of the regular black hole in this context.