# Test of quantum atmosphere in the dimensionally reduced Schwarzschild black hole

## TL;DR

This paper confirms that Hawking radiation originates from a quantum atmosphere near the black hole horizon in a dimensionally reduced Schwarzschild model, rather than directly at the horizon itself.

## Contribution

It provides an exact calculation demonstrating the quantum atmosphere as the source of Hawking radiation in an analytically solvable model.

## Key findings

- Hawking radiation peaks at a quantum atmosphere outside the horizon.
- Out-temperature vanishes at the horizon and peaks at a scale set by the horizon radius.
- The out-temperature approaches the Hawking temperature at infinity.

## Abstract

It has been suggested by Giddings that the origin of Hawking radiation in black holes is a quantum atmosphere of near-horizon quantum region by investigating both the total emission rate and the stress tensor of Hawking radiation. Revisiting this issue in the exactly soluble model of a dimensionally reduced Schwarzschild black hole, we shall confirm that the dominant Hawking radiation in the Unruh vacuum indeed occurs at the quantum atmosphere, not just at the horizon by exactly calculating the out-temperature responsible for outgoing Hawking particle excitations. Consequently we show that the out-temperature vanishes at the horizon and has a peak at a scale whose radial extent is set by the horizon radius, and then decreases to the Hawking temperature at infinity. We also discuss bounds of location of the peak for the out-temperature in our model.