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The ultrarelativistic limit of 2D dilaton gravity and its energy–momentum tensor

The ultrarelativistic limit of two-dimensional dilaton gravity is presented and its associated (anti-)self-dual energy–momentum tensor is derived. It is localized on a null line, although the line element remains twice differentiable. Relations to the Aichelburg–Sexl spacetime and constant dilaton vacua are pointed out. Geodesics are found to be smooth for minimally coupled test particles but non-smooth—with a finite jump in the acceleration—for test particles coupled non-minimally to the dilaton. Quantization on boosted backgrounds is discussed; no anomalous trace of the energy–momentum tensor arises and the 1-loop flux component can be adjusted to be equal to the classical flux of the shock wave.