# On Reflectivity of Quantum Black Hole Horizons

## TL;DR

This paper investigates the quantum properties of black hole horizons, revealing a universal flux reflectivity linked to Hawking temperature, predicting observable echoes in black hole ringdowns, and modifying membrane paradigm viscosity at quantum scales.

## Contribution

It introduces a universal flux reflectivity formula for quantum black hole horizons and explores its implications for black hole physics and observable phenomena.

## Key findings

- Universal flux reflectivity given by a Boltzmann factor
- Predicted echoes in Kerr black hole ringdowns
- Modified membrane viscosity at quantum frequencies

## 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 ${\mathcal R} = \exp\left(-{\hbar |\omega| \over k T_{\rm H}}\right)$, where $\omega$ 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 $\eta = \frac{c^3}{16\pi G}\tanh\left({\hbar |\omega| \over 4 k T_{\rm H}}\right)$, only approaching General Relativistic value at high frequencies.