Planckian physics comes into play at Planckian distance from horizon

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.

UV And IR Effects On Hawking Radiation

“…It was explained in Ref. [15] that the momentum conservation of P U is only approximately observed in a way compatible with the uncertainty relation ∆P u ∆P U P u e u/2a /a, since P u and P U do not commute. The uncertainty relation admits a large violation of momentum conservation of P U at large u.…”

“…The origin of this effect is a Lorentz-invariant trans-Planckian energy between the outgoing quantum modes and the collapsing matter. Even though the outgoing modes are still virtual particles at the horizon (hence the horizon remains uneventful as demanded by the nice-slice argument), their time evolution through the collapsing matter relies on trans-Planckian physics [15]. On the other hand, in agreement with the nice-slice argument, the horizon is uneventful for freely falling observers [15].…”

“…Although this amplitude was already calculated in Refs. [15,39,40], we shall revisit this problem by examining the time-evolution of the Unruh vacuum in the Hamiltonian formulation, so that we can clearly see how the vacuum state evolves towards multi-particle states. For simplicity, we shall adopt the light-cone frame for this calculation.…”

“…However, it was recently found [15] that higher-derivative interactions with the background geometry or collapsing matter modify Hawking radiation by an exponentially growing rate of particle production. (The effect of renormalizable interactions on Hawking radiation was considered in Ref.…”

“…In Sec.4, we reproduce the large amplitude of particle production mentioned above [15] via a different approach. We adopt the Hamiltonian formulation to show how the Unruh vacuum evolves into a superposition of multi-particle states.…”