Equal-time vacuum correlations of a test quantum field on a dynamically collapsing, horizon-forming spacetime develop non-local peaks across the apparent horizon, and the outside peak moves away from the horizon over time.
On the origin of the particles in black hole evaporation
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abstract
We present an analytic derivation of Hawking radiation for an arbitrary (spatial) dispersion relation $\omega(k)$ as a model for ultra-high energy deviations from general covariance. It turns out that the Hawking temperature is proportional to the product of the group $d\omega/dk$ and phase $\omega/k$ velocities evaluated at the frequency $\omega$ of the outgoing radiation far away, which suggests that Hawking radiation is basically a low-energy phenomenon. Nevertheless, a group velocity growing too fast at ultra-short distances would generate Hawking radiation at ultra-high energies (``ultra-violet catastrophe'') and hence should not be a realistic model for the microscopic structure of quantum gravity.
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Non-local correlations of a test quantum field in gravitational collapse
Equal-time vacuum correlations of a test quantum field on a dynamically collapsing, horizon-forming spacetime develop non-local peaks across the apparent horizon, and the outside peak moves away from the horizon over time.