Quantum Transparency of Near-extremal Black Holes

TL;DR

This work shows that near-extremal Reissner-Nordström black holes in a low-temperature, Schwarzian-dominated throat exhibit a spin-induced energy gap that creates transparency windows for low-frequency, fixed-helicity EM and gravitational waves. By coupling external fields to the AdS$_2$ throat and using Schwarzian transition rates, the authors derive a general quantum greybody factor that unifies the quantum absorption with the semiclassical limit and provide explicit results for the $\ell=1$ photon and $\ell=2$ graviton. The key finding is quantum translucency: below the gap the black hole is transparent, and above it the absorption remains strongly suppressed because final-state densities are scarce, though transition rates are enhanced. The results imply that quantum black holes can be probed through low-frequency radiation and that spin quantization introduces universal features across charged and rotating near-extremal black holes, with potential extensions to other conserved charges and higher-dimensional spacetimes.

Abstract

We investigate the scattering of electromagnetic and gravitational waves off a Reissner-Nordström black hole in the low-temperature regime where the near-horizon throat experiences large quantum fluctuations. We find that the black hole is transparent to electromagnetic and gravitational radiation of fixed helicity below a certain frequency threshold. This phenomenon arises because the angular momentum of the black hole is quantized, creating an energy gap between the spinless black hole state and the first excited spinning states. Radiation with angular momentum -- such as photons, gravitons, and partial waves of a massless scalar field, which we also study -- must supply enough energy to bridge this gap to be absorbed. Below this threshold, no absorption can occur, rendering the black hole transparent. For frequencies above the gap, the scarcity of black hole states continues to suppress the absorption cross-section relative to semiclassical predictions, making the black hole translucent rather than completely transparent. Notably, electromagnetic absorption is significantly stronger than gravitational absorption, beyond what differences in spin alone would suggest.

Figures (5)

• Figure 1: Electromagnetic and gravitational quantum transparency. We show the quantum absorption cross-section of photon waves with $\ell=1$ (left) and graviton waves with $\ell=2$ (right) as a function of their frequency $\omega$, for two different values of the initial black hole energy above extremality, $E_i = 0.6 \, E_b$ (orange) and $E_i = 0.8 \, E_b$ (red) (see eqs. \ref{['eq:l1Ph']} and \ref{['eq:l2Gr']}). The transparency window \ref{['gapell']} for $E_i = 0.6 \, E_b$ extends up to $\omega/E_i \approx 0.67$ for photons and $\omega/E_i = 4$ for gravitons. For $E_i = 0.8 \, E_b$, it extends to $\omega/E_i = 0.25$ for photons and $\omega/E_i = 2.75$ for gravitons. For the comparison between photon and graviton absorption, see Fig. \ref{['fig:l1Ph_vs_l2Gr']}. The quantum and semiclassical predictions are compared in Figs. \ref{['fig:l1Ph_qu_vs_sc']} and \ref{['fig:l1Ph_f_rho']}. In all these figures, the cross-sections are expressed in units of $E_b^{6}\, r_0^{8} = (\pi/S_0)^{6} r_0^2$, which is much smaller than the horizon area $\propto r_0^2$. This reflects the general suppression of low-frequency absorption for spinning fields, an effect that is further accentuated in the quantum regime by the strong depletion of available black hole states.
• Figure 2: Quantum absorption cross-section of $\ell = 1$ photon \ref{['eq:l1Ph']} (red) vs. $\ell = 2$ graviton \ref{['eq:l2Gr']} (blue) as a function of $\omega$ for a black hole with $E_i = 0.8 \, E_b$. The photon cross-section has been reduced by a factor of $10^{-4}$ to bring it within the figure---see the text for the explanation of the dramatic enhancement of the photon absorption. The transparency window \ref{['eq:transp_cond']} for the photon ends at $\omega / E_i = 0.25$ (not visible in the figure), while for the graviton it ends at $\omega/E_i = 2.75$.
• Figure 3: Field-type-independent absorption cross-section $\widehat{\sigma}$ (cf. \ref{['eq:sigmahat']}) as a function of $\omega$ for $E_i = 0.8 \, E_b$. Left: plot at fixed $\ell = 1$ for different $\Delta$. Right: plot at fixed $\Delta = 3$ for different $\ell$. In the quantum regime where $\omega/E_i\lesssim \mathcal{O}(1)$ (say, $\omega/E_i \le 5$), but above the transparency window for the $\ell = 2$ graviton, which ends at $\omega/E_i = 2.75$, the cross-section becomes higher as we increase $\Delta$, and as we decrease $\ell$. The same qualitative feature is observed for fixed $\ell = 2$, or for fixed $\Delta = 2$. The length unit for $\widehat{\sigma}$ is $E_b^{\Delta+\ell-1}\, r_0^{\Delta+\ell}$.
• Figure 4: Quantum \ref{['eq:l1Ph']} (red) vs. semiclassical \ref{['eq:Pgb_full_sc_l1_photon']} (black) absorption cross-section of the $\ell = 1$ photon as a function of $\omega$, for $E_i = 0.8 \, E_b$. The quantum transparency window \ref{['eq:transp_cond']} ends at $\omega / E_i = 0.25$ and is not easily distinguishable. Note how the quantum cross-section is always suppressed compared to the semiclassical one, giving rise to quantum translucency.
• Figure 5: Quantum vs. semiclassical absorption transition probabilities (left) and density of final states (right) of the $\ell = 1$ photon as a function of $\omega$, for $E_i = 0.8 \, E_b$ (eqs. \ref{['eq:f_qu']}--\ref{['eq:rho_sc']}). The transparency window \ref{['eq:transp_cond']} ends at $\omega / E_i = 0.25$. As in the case of the $\ell = 0$ scalar Emparan:2025sao, quantum fluctuations markedly enhance absorption transitions while sharply suppressing the density of final states. These competing effects determine whether the absorption cross-section is enhanced or suppressed, the latter being the case for spinning radiation. We plot $f_3$ in units of $e^{-S_0} E_b^6$, and $\rho_1$ in units of $e^{S_0} E_b^{-1}$. The log-scale vertical axes highlight the large disparity between semiclassical and quantum values.