Holographic integral geometry with time dependence

We write down Crofton formulas–expressions that compute lengths of spacelike curves in asymptotically AdS${}_3$ geometries as integrals over kinematic space–which apply when the curve and/or the background spacetime is time-dependent. Relative to their static predecessor, the time-dependent Crofton formulas display several new features, whose origin is the local null rotation symmetry of the bulk geometry. In pure AdS${}_3$ where null rotations are global symmetries, the Crofton formulas simplify and become integrals over the null planes, which intersect the bulk curve.