An order-unity correction to Hawking radiation

Understand

When a black hole first forms, the properties of the emitted radiation as measured by observers near future null infinity are very close to the 1974 prediction of Hawking.

• However, deviations grow with time, and become of order unity after a time $t \sim M_i^{7/3}$, where $M_i$ is the initial mass in Planck units.
• After an evaporation time the corrections are large: the angular distribution of the emitted radiation is no longer dominated by low multipoles, with an exponential fall off at high multipoles.
• Instead, the radiation is redistributed as a power law spectrum over a broad range of angular scales, all the way down to the scale $\Delta \theta \sim 1/M_i$, beyond which there is exponential falloff.