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 ${\mathcal R} = \exp\left(-{\hbar |ω| \over k T_{\rm H}}\right)$, where $ω$ is frequency in the horizon frame and $T_{\rm H}$ is the Hawking temperature. This implies CP-symmetry (or $\bf{RP}^3$ 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 $η= \frac{c^3}{16πG}\tanh\left({\hbar |ω| \over 4 k T_{\rm H}}\right)$, only approaching General Relativistic value at high frequencies.

15 pages, 5 figures, appendixes added