Grey-body factors of higher dimensional regular black holes in quasi-topological theories

TL;DR

Grey-body factors of higher-dimensional regular black holes in quasi-topological gravity are computed by solving Maxwell-field perturbations in D-dimensional backgrounds with infinite-curvature corrections that regularize the core. The master equations reduce to Schrödinger-like wave equations with effective potentials $V_S$ and $V_V$, and grey-body factors $\Gamma_{\ell}(\omega)$ are obtained via a high-order WKB analysis (up to order $N=5$) supplemented by a two-mode quasinormal-mode estimate. The results show that higher-curvature corrections raise and broaden the potential barrier, suppress low-frequency transmission, and decrease the Hawking temperature $T_H$; consequently the electromagnetic energy-emission rate is exponentially suppressed as $\alpha$ grows, with spectra shifting to lower frequencies. An evaporation analysis indicates a transition from Schwarzschild-like complete evaporation ($\alpha=0$) to asymptotic remnants at maximal $\alpha$, implying observable signatures and motivating extension to gravitational perturbations.

Abstract

We study grey-body factors and Hawking radiation of higher-dimensional regular black holes arising in quasi-topological gravity. These spacetimes incorporate infinite-curvature corrections that remove the central singularity while preserving an event horizon and a well-defined semiclassical description. We show that, for all considered regular black hole models, the transmission of radiation and the corresponding Hawking evaporation are significantly suppressed compared to the singular black hole solutions of General Relativity.

Figures (4)

• Figure 1: Difference between WKB approximations of various orders and the accurate grey-body data for electromagnetic perturbations of the $D=5$ black hole $(f)$ for $\ell=1$ and $\alpha=0.3r_0^2$: $V_S$ (\ref{['eq:V1']}) (top panel) and $V_V$ (\ref{['eq:V2']}) (bottom panel). Accurate data are taken from Ref. Konoplya:2025uta.
• Figure 2: Transmission coefficients for electromagnetic perturbations of the $D=5$ black hole $(f)$: $V_{S}$ (\ref{['eq:V1']}) (top panel) and $V_{V}$ (\ref{['eq:V2']}) (bottom panel). The curves show the dependence on the parameter $\alpha = 0, 0.1, \ldots, 0.6, 0.66$, increasing from darker to lighter tones.
• Figure 3: Hawking temperature with $D=5$ and $r_{0}=1$ for various regular black holes: black line $(a)$, grey line $(b)$, blue line $(c)$, red line $(d)$, pink line $(e)$, and orange line $(f)$.
• Figure 4: Energy emission rates for the electromagnetic perturbations of the $D=5$ black hole $(f)$: $V_{S}$ (\ref{['eq:V1']}) (top panel) and $V_{V}$ (\ref{['eq:V2']}) (bottom panel), for different values of the parameter $\alpha$.