Light-ray operators, detectors and gravitational event shapes

Light-ray operators naturally arise from integrating Einstein equations at null infinity along the light-cone time. We associate light-ray operators to physical detectors on the celestial sphere and we provide explicit expressions in perturbation theory for their hard modes using the steepest descent technique. We then study their algebra in generic 4-dimensional QFTs of massless particles with integer spin, comparing with complexified Cordova-Shao algebra. For the case of gravity, the Bondi news squared term provides an extension of the ANEC operator at infinity to a shear-inclusive ANEC, which as a quantum operator gives the energy of all quanta of radiation in a particular direction on the sky. We finally provide a direct connection of the action of the shear-inclusive ANEC with detector event shapes and we study infrared-safe gravitational wave event shapes produced in the scattering of massive compact objects, computing the energy flux at infinity in the classical limit at leading order in the soft expansion.