On reflectivity of quantum black hole horizons

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 R = exp (- (h) over bar vertical bar(omega) over tilde vertical bar/kT(H)), where (omega) over tilde is frequency in the horizon frame and T-H is the Hawking temperature. This implies CP-symmetry (or RP3 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 = c(3)/16 pi G tanh (- (h) over bar vertical bar(omega) over tilde vertical bar/kT(H)), only approaching General Relativistic value at high frequencies.