Quantum gravitational corrections to particle creation by black holes
X. Calmet, S. Hsu, M. Sebastianutti
We calculate quantum gravitational corrections to the amplitude for the emission of a Hawking particle by a black hole. We show explicitly how the amplitudes depend on quantum corrections to the exterior metric (quantum hair). This reveals the mechanism by which information escapes the black hole. The quantum state of the black hole is reflected in the quantum state of the exterior metric, which in turn influences the emission of Hawking quanta.In earlier work we showed that the quantum state of a black hole is reflected in the quantum state of the exterior metric (outside the horizon). This violates classical intuitions, but can be shown explicitly using long wavelength effective field theory.
We calculated examples of small corrections to the external spacetime geometry which are sensitive to the internal BH state. In this paper we show that these corrections in turn affect Hawking radiation amplitudes.
This means that the Hawking radiation state depends on the internal BH state. At the quantum level the hole is not so black! We derive the results using both Hawking's original method and the tunneling method of Parikh and Wilczek.
While the focus of the new paper is explicit calculations, the big picture statement is:
The quantum state of the BH is reflected in the quantum state of its external gravitational field, which forms the background where the Hawking radiation originates. Radiation amplitudes are NOT independent of interior state.