We calculate the vacuum expectation value, $T_{\mu \nu }$, of the energy-momentum tensor of a massless scalar field in a general two-dimensional spacetime and evaluate it in a two-dimensional model of gravitational collapse. In two dimensions, quantum radiation production is incompatible with a conserved and traceless $T_{\mu \nu }$. We there-fore resolve an ambiguity in our expression for $T_{\mu \nu }$, regularized by a geodesic point-separation procedure, by demanding conservation but allowing a trace. In the collapse model, the results support that picture of black-hole evaporation in which pairs of particles are created outside the horizon (and not entirely in the collapsing matter), one of which carries negative energy into the future horizon of the black hole, while the other contributes to the thermal flux at infinity.

• Received 11 August 1975

DOI:https://doi.org/10.1103/PhysRevD.13.2720