Quantum Geometry of the Light Cone

Abstract:  In relativity, the geometry of the light cones determines the causal structure of spacetime. Under the influence of gravity, the light cones bend and curve. A previously expanding light cone can fall back into itself. In this way, the causal structure becomes a dynamical aspect of spacetime. How do we understand this link between gravity, geometry and causality at the quantum level? Is there a quantum light cone geometry? In my talk, I will argue that the answer to this problem is crucial for making progress in quantum gravity. It is, in fact, a problem that is shared among different approaches, from holography, to celestial amplitudes and loop quantum gravity. In my presentation, I report on three new results on this frontier. First, I provide a non-perturbative characterization of impulsive gravitational null initial data for tetradic gravity on a light cone. Second, the description is taken to the quantum level. Third, an immediate physical implication is found: in the model, the Planck luminosity separates the eigenvalues of the radiated power. Below the Planck power, the spectrum of the radiated power is discrete. Above the Planck power, the spectrum is continuous and the resulting physical states contain caustics that can spoil the semi-classical limit.  The talk is based on arXiv:2402.12578, arXiv:2401.17491, arXiv:2104.05803.