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

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.