Résumé

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.

page Indico de l'événement