Abstract
We consider gravity in 3+1 spacetime dimensions coupled to N scalar matter fields in a semiclassical limit where . The dynamical evolution of a black hole including the back-reaction of the Hawking radiation on the metric is formulated as an initial-value problem. The quantum stress-energy tensor is evaluated using a point-splitting regularization along spacelike geodesics. To account for the quantum entanglement of the matter fields, they are treated as a set of bilocal collective fields defined on spacelike hypersurfaces. The resulting semiclassical field equations include terms up to fourth order in derivatives that can be treated in a perturbative expansion. The formulation we arrive at should be amenable to numerical simulation of time-dependent semiclassical spacetime.
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