Semiclassical Dynamics of Hawking Radiation

Abstract

We consider gravity in 3+1 spacetime dimensions coupled to $N$ scalar matter fields in a semiclassical limit where $N\to \infty$. 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 $\hslash$ expansion. The formulation we arrive at should be amenable to numerical simulation of time dependent semiclassical spacetime.

27 pages

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Cited by in corpus (1)

• Mixture equivalence principles and post-quantum theories of gravity