Semiclassical Dynamics of Hawking Radiation

TL;DR

This paper develops a semiclassical framework for analyzing the dynamical evolution of black holes in 3+1 dimensions, incorporating back-reaction from Hawking radiation and quantum entanglement effects, suitable for numerical simulation.

Contribution

It introduces a novel initial value formulation for black hole evolution with quantum back-reaction, using bilocal fields and higher-derivative semiclassical equations.

Findings

Formulated a set of semiclassical field equations including quantum entanglement effects.

Derived a perturbative expansion in ar for the equations.

Established a basis for numerical simulation of time-dependent semiclassical spacetimes.

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 $\hbar$ expansion. The formulation we arrive at should be amenable to numerical simulation of time dependent semiclassical spacetime.