Recently, I introduced a non-perturbative quantization of
impulsive gravitational null initial data. In this talk, I present the
key results established thus far. The starting point is the
characteristic null initial problem for tetradic gravity with a
parity-odd Holst term in the bulk. After a basic review about the
resulting Carrollian boundary field theory, I will introduce a specific
class of impulsive radiative data. This class is defined for a specific
choice of relational clock. The clock is chosen in such a way that the
shear of the null boundary follows the profile of a step function. The
angular dependence is arbitrary. Next, I explain how to solve the
residual constraints, which are the Raychaudhuri equation and a
Carrollian transport equation for an SL(2,R) holonomy. The resulting
submanifold in phase space is symplectic. Along each null generator, we
end up with a simple mechanical system. The quantization of this system
is straightforward. The physical Hilbert space is the kernel of a
constraint, which is a combination of ladder operators. Solving the
constraint amounts to imposing a simple recurrence relation for physical
states. One of the quantum numbers is the total luminosity carried to
infinity. I show that a transition happens when the luminosity reaches
the Planck power. Below the Planck power, the spectrum of the radiated
power is discrete. Above the Planck power, the spectrum is continuous
and contains caustics that can be avoided only when the spectrum is
discrete.
