The horizon of the lightest black hole

We study the properties of the poles of the resummed graviton propagator obtained by resumming bub- ble matter diagrams which correct the classical graviton prop- agator. These poles have been previously interpreted as black holes precursors. Here, we show using the horizon wave- function formalism that these poles indeed have properties which make them compatible with being black hole precur- sors. In particular, when modeled with a Breit–Wigner dis- tribution, they have a well-defined gravitational radius. The probability that the resonance is inside its own gravitational radius, and thus that it is a black hole, is about one half. Our results confirm the interpretation of these poles as black hole precursors.