In this paper we study the BMS symmetry of the celestial OPE of two positive helicity gravitons in Einstein theory in four dimensions. The celestial OPE is obtained by Mellin transforming the scattering amplitude in the (holomorphic) collinear limit. The collinear limit at leading order gives the singular term of the celestial OPE. We compute the first subleading correction to the OPE by analysing the four graviton scattering amplitude directly in Mellin space. The subleading term can be written as a linear combination of BMS descendants with the OPE coefficients determined by BMS algebra and the coefficient of the leading term in the OPE. This can be done by defining a suitable BMS primary state. We find that among the descendants, which appear at the first subleading order, there is one which is created by holomorphic supertranslation with simple pole on the celestial sphere.

We show how to compute classical wave observables using quantum scattering amplitudes. We discuss observables both with incoming and with outgoing waves. The required classical limits are naturally described by coherent states of massless bosons. We recompute the classic gravitational deflection of light, and also show how to rederive Thomson scattering. We introduce a new class of local observables, which includes the asymptotic electromagnetic and gravitational Newman-Penrose scalars. As an example, we compute a simple radiated waveform: the expectation of the electromagnetic field in charged-particle scattering. At leading order, the waveform is trivially related to the five-point scattering amplitude.

We study the variance in the measurement of observables during scattering events, as computed using amplitudes. The classical regime, characterised by negligible uncertainty, emerges as a consequence of an infinite set of relationships among multileg, multiloop amplitudes in a momentum-transfer expansion. We discuss two non-trivial examples in detail: the six-point tree and the five-point one-loop amplitudes in scalar QED. We interpret these relationships in terms or a coherent exponentiation of radiative effects in the classical limit which generalises the eikonal formula, and show how to recover the impulse, including radiation reaction, from this generalised eikonal. Finally, we incorporate the physics of spin into our framework.

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In the two-body scattering problem in general relativity, we study the final graviton particle distribution using a perturbative approach. We compute the mean, the variance and the factorial moments of the distribution from the expectation value of the graviton number operator in the KMOC formalism. For minimally coupled scalar particles, the leading deviation from the Poissonian distribution is given by the unitarity cut involving the six-point tree amplitude with the emission of two gravitons. We compute this amplitude in two independent ways. First, we use an extension of the Cheung-Remmen parametrization that includes minimally coupled scalars. We then repeat the calculation using on-shell BCFW-like techniques, finding complete agreement. In the classical limit, this amplitude gives a purely quantum contribution, proving that we can describe the final semiclassical radiation state as a coherent state at least up to order $$ \mathcal{O} $$ O (G4) for classical radiative observables. Finally, we give general arguments about why we expect this to hold also at higher orders in perturbation theory.

We explore the celestial holography proposal for non-trivial asymptotically flat backgrounds including the Coulomb field of a static and spinning point charge, their gravitational counterparts described by the Schwarzschild and Kerr metrics, as well as the Aichelburg-Sexl shockwave and spinning shockwave geometries and their electromagnetic cousins. We compute celestial two-point amplitudes on these Kerr-Schild type backgrounds which have the desirable feature, due to the presence of an external source, that they are non-vanishing for general operator positions and are not constrained by the kinematic delta functions of flat space celestial CFT correlators. Of particular interest is the case of shockwave backgrounds where the two-point scattering amplitude of massless scalars can be interpreted as a standard CFT three-point correlator between two massless asymptotic states and a conformal primary shockwave operator. We furthermore show that the boundary on-shell action for general backgrounds becomes the generating functional for tree-level correlation functions in celestial CFT. Finally, we derive (conformal) Faddeev-Kulish dressings for particle-like backgrounds which remove all infrared divergent terms in the two-point functions to all orders in perturbation theory.

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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.