Black hole's quantum N‐portrait

We establish a quantum measure of classicality in the form of the occupation number, N, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose‐condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, N is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by N. The black hole is a leaky bound‐state in form of a cold Bose‐condensate of N weakly‐interacting soft gravitons of wave‐length √N times the Planck length and of quantum interaction strength 1/N. Such a bound‐state exists for an arbitrary N. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non‐Wilsonian UV‐self‐completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose‐condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature T = 1/(√N). The Bekenstein entropy originates from the exponentially growing with N number of quantum states. Finally, our quantum picture allows to understand classicalization of deep‐UV gravitational scattering as 2 → N transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft‐Polyakov monopole. Both objects represent Bose‐condensates of N soft bosons of wavelength √N and interaction strength 1/N. In short, the semi‐classical black hole physics is 1/N‐coupled large‐N quantum physics.