Null Musings

One of the main achievements of my last four years at Perimeter has been the development and formulation of intrinsic null geometry. This framework has served as a common denominator for the study of the (algebraic) quantization of gravity on null hypersurfaces; connections to quantum-gravity phenomenology for causal diamonds and the derivation of the Verlinde-Zurek fluctuation identity; a complete characterization of the null gravitational phase space; links to asymptotic null infinity; and the related classification of eBMS anomalies. After introducing the basic toolkit of null geometry, I will digress on Carrollian connections and on how the intrinsic geometry is related to an ambient manifold. I will then introduce the null Brown-York stress tensor, which allows the intrinsic gravitational constraints to be recast as conservation laws. Finally, I will briefly retrace the path through the aforementioned applications, with particular emphasis on new and ongoing results.