  We investigate Hawking evaporation in a recently suggested picture in which
black holes are Bose condensates of gravitons at a quantum critical point.
There, evaporation of a black hole is due to two intertwined effects. Coherent
excitation of a tachyonic breathing mode is responsible for the collapse of the
condensate, while incoherent scattering of gravitons leads to Hawking
radiation. To explore this, we consider a toy model of a single bosonic degree
of freedom with derivative self-interactions. We consider the real-time
evolution of a condensate and derive evaporation laws for two possible decay
mechanisms in the Schwinger-Keldysh formalism. We show that semiclassical
results can be reproduced if the decay is due to an effective two-body process,
while the existence of a three-body channel would imply very short lifetimes
for the condensate. In either case, we uncover the existence of scaling
solutions in which the condensate is at a critical point throughout the
collapse. In the case of a two-body decay we moreover discover solutions that
exhibit the kind of instability that was recently conjectured to be responsible
for fast scrambling.
