Tue, 09.04.2024 14:00

Quantum Geometry of the Light Cone

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.



Speaker: Wolfgang Wieland (FAU Erlangen-Nürnberg)


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