In general relativity, the Aichelburg–Sexl ultraboost is an exact solution which models the spacetime of an observer moving towards or away from a spherically symmetric gravitating object at nearly the speed of light.
The original motivation behind the ultraboost was to consider the gravitational field of massless point particles within general relativity.
The metric tensor can be written, in terms of Brinkmann coordinates, as The ultraboost can be obtained as the limit of a metric, which is also an exact solution, at least if one admits impulsive curvatures.
In these plus-polarized axisymmetric vacuum pp-waves, the curvature is concentrated along the axis of symmetry, falling off like
, the wave profile turns into a Dirac delta and the ultraboost is recovered.