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Models for gamma-ray burst afterglow dynamics and synchrotron spectra areknown to exhibit various scale invariances, owing to the scale-free nature offluid dynamics and the power-law shape of synchrotron spectra. Since theobservations of a gamma-ray burst and afterglow directly associated with thedetection of gravitational waves from a neutron star merger (GW170817),off-axis jet models including a lateral energy structure in the initial outflowgeometry have gained in prominence. Here we demonstrate how scale-invariancecarries over to arbitrary jet structure and dynamical stages. We provideafterglow flux expressions for arbitrary light curve slope and jet structureand demonstrate how these can be used to quickly assess the physicalimplications of afterglow observations. We show how the late Deep Newtonianafterglow stage remains scale-invariant but adds distinct spectral scalingregimes. Finally, we show that for given jet structure a universal curve can beconstructed of the centroid offset (that can be measured using very-largebaseline interferometry) versus observer angle, in a manner independent ofexplosion energy and circumburst density. Our results apply to any synchrotrontransient characterized by a release of energy in an external medium, includingsupernova remnants, kilonova afterglows and soft gamma-repeater flares.

Scaling relations for gamma-ray burst afterglow light curves and centroid motion independent of jet structure and dynamics