A gravitationally collapsed object can bounce out from its horizon via a tunnelling process that violates the classical equations in a finite region. Since tunnelling is a nonperturbative phenomenon, it cannot be described in terms of quantum fluctuations around a classical solution, and a background-free formulation of quantum gravity is needed to analyze it. Here, we use loop quantum gravity to compute the amplitude for this process, in a first approximation. The amplitude determines the tunnelling time as a function of the mass. This is the key information to evaluate the relevance of this process for the interpretation of fast radio bursts or high-energy cosmic rays. The calculation offers a template and a concrete example of how a background-free quantum theory of gravity can be used to compute a realistic observable quantity.

• Received 2 August 2016

DOI:https://doi.org/10.1103/PhysRevD.94.084035