The power emitted by a Schwarzschild black hole via Bekenstein-Hawking radiation is usually given for an observer at spatial infinity.
What is the emitted power for an observer hovering just above its horizon at a radial distance $r$? (Here, "emitted" is meant to describe only the flow of energy away from the black hole.)
An observer nearer to the horizon will see a higher temperature $T$, due to red shift. In all cases, the emitted power $P(r)$ at radius $r$ is expected to be given by the black hole horizon surface times $T^4$ times the Stefan-Boltzmann constant.
The emitted power should thus increase when getting closer to the horizon. What is the value of $P(r)$?