Abstract
In the background of a gravitational collapse, we compute the transition amplitudes for the creation of particles for distant observers due to higher-derivative interactions in addition to Hawking radiation. The amplitudes grow exponentially with time and become of order 1 when the collapsing matter is about a Planck length outside the horizon. As a result, the effective theory breaks down at the scrambling time, invalidating its prediction of Hawking radiation. Planckian physics comes into play to decide the fate of black-hole evaporation.
Highlights
Planckian physics comes into play to decide the fate of black-hole evaporation
We consider outgoing particles with energies ∼ O(1/a) because states including them must exist in order for the effective theory to predict Hawking radiation. (Here, a ≡ 2GN M is the Schwarzschild radius, where GN is the Newton constant and M is the black hole mass.)
Because of this uncertainty principle, momentum conservation for freely falling observers hardly restricts the creation of outgoing particles for distant observers
Summary
We consider the gravitational collapse of a null thin shell at v = vs, so the metric (2.1) holds only for v ≥ vs. In the near-horizon region where 0 < r − a a, the Schwarzschild metric is approximately ds2 −dU dV + r2dΩ2,. We have used the same symbols (U, V ) for these coordinates because they can be identified with the Kruskal coordinates (2.4) and (2.5) across the collapsing shell in the near-horizon region. The creation-annihilation operators (a†Ω, aΩ) are defined with respect to the Kruskal coordinate U , and (b†ω, bω) those defined with respect to fiducial observers (or distant observers). They are related to each other via the Bogoliubov transformation bω =. Hawking radiation can be described in terms of 0|b†(ω0,u0)b(ω0,u0)|0 for a given wave packet, which is proportional to the Planck distribution [10]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
