  We revisit the connection between Hawking radiation and high-frequency
dispersions for a Schwarzschild black hole following the work of Brout et al..
After confirming the robustness of Hawking radiation for monotonic dispersion
relations, we consider non-monotonic dispersion relations that deviate from the
standard relation only in the trans-Planckian domain. Contrary to the common
belief that Hawking radiation is insensitive to UV physics, it turns out that
Hawking radiation is subject to significant modifications after the scrambling
time. Depending on the UV physics at the singularity, the amplitude of Hawking
radiation could diminish after the scrambling time, while the Hawking
temperature remains the same. Our finding is thus not contradictory to earlier
works regarding the robustness of Hawking temperature.
