On Reflectivity of Quantum Black Hole Horizons

Abstract

We study the reflectivity of quantum black hole (BH) horizons using detailed balance and fluctuation-dissipation theorem, finding a universal flux reflectivity given by the Boltzmann factor $\mathcal{R}=\exp \left(-\frac{\hslash |\omega |}{k{T}_{\mathrm{H}}}\right)$, where $\omega$ is frequency in the horizon frame and $T_{\mathrm{H}}$ is the Hawking temperature. This implies CP-symmetry (or ${\mathbf{RP}}^3$ topology) of the extended BH spacetime. We then briefly discuss related physical implications: We predict echoes in the ringdown of Kerr BHs, but they do not exhibit ergoregion instability. The viscosity in the membrane paradigm is modified to $\eta =\frac{c^3}{16\pi G}\tanh \left(\frac{\hslash |\omega |}{4k{T}_{\mathrm{H}}}\right)$, only approaching General Relativistic value at high frequencies.

15 pages, 5 figures, appendixes added