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Description

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.

The agenda of this meeting is empty