%0 Journal Article %1 hod2016hawking %A Hod, Shahar %D 2016 %K black_holes gr %T Hawking radiation and the Stefan-Boltzmann law: The effective radius of the black-hole quantum atmosphere %U http://arxiv.org/abs/1607.02510 %X It has recently been suggested S. B. Giddings, Phys. Lett. B 754, 39 (2016) that the Hawking black-hole radiation spectrum originates from an effective quantum ätmosphere" which extends well outside the black-hole horizon. In particular, comparing the Hawking radiation power of a $(3+1)$-dimensional Schwarzschild black hole of horizon radius $r_H$ with the familiar Stefan-Boltzmann radiation power of a $(3+1)$-dimensional flat space perfect blackbody emitter, Giddings concluded that the source of the Hawking semi-classical black-hole radiation is a quantum region outside the Schwarzschild black-hole horizon whose effective radius $r_A$ is characterized by the relation $\Delta rr_A-r_H\sim r_H$. It is of considerable physical interest to test the general validity of Giddings's intriguing conclusion. To this end, we study the Hawking radiation of $(D+1)$-dimensional Schwarzschild black holes. We find that the dimensionless radii $r_A/r_H$ which characterize the black-hole quantum atmospheres, as determined from the Hawking black-hole radiation power and the $(D+1)$-dimensional Stefan-Boltzmann radiation law, are a decreasing function of the number $D+1$ of spacetime dimensions. In particular, it is shown that radiating $(D+1)$-dimensional Schwarzschild black holes are characterized by the relation $(r_A-r_H)/r_Hłl1$ in the large $D\gg1$ regime. Our results therefore suggest that, at least in some physical cases, the Hawking emission spectrum originates from quantum excitations very near the black-hole horizon.

@article{hod2016hawking, abstract = {It has recently been suggested [S. B. Giddings, Phys. Lett. B {\bf 754}, 39 (2016)] that the Hawking black-hole radiation spectrum originates from an effective quantum "atmosphere" which extends well outside the black-hole horizon. In particular, comparing the Hawking radiation power of a $(3+1)$-dimensional Schwarzschild black hole of horizon radius $r_{\text{H}}$ with the familiar Stefan-Boltzmann radiation power of a $(3+1)$-dimensional flat space perfect blackbody emitter, Giddings concluded that the source of the Hawking semi-classical black-hole radiation is a quantum region outside the Schwarzschild black-hole horizon whose effective radius $r_{\text{A}}$ is characterized by the relation $\Delta r\equiv r_{\text{A}}-r_{\text{H}}\sim r_{\text{H}}$. It is of considerable physical interest to test the general validity of Giddings's intriguing conclusion. To this end, we study the Hawking radiation of $(D+1)$-dimensional Schwarzschild black holes. We find that the dimensionless radii $r_{\text{A}}/r_{\text{H}}$ which characterize the black-hole quantum atmospheres, as determined from the Hawking black-hole radiation power and the $(D+1)$-dimensional Stefan-Boltzmann radiation law, are a decreasing function of the number $D+1$ of spacetime dimensions. In particular, it is shown that radiating $(D+1)$-dimensional Schwarzschild black holes are characterized by the relation $(r_{\text{A}}-r_{\text{H}})/r_{\text{H}}\ll1$ in the large $D\gg1$ regime. Our results therefore suggest that, at least in some physical cases, the Hawking emission spectrum originates from quantum excitations very near the black-hole horizon.}, added-at = {2016-07-12T20:20:17.000+0200}, author = {Hod, Shahar}, biburl = {https://www.bibsonomy.org/bibtex/2d0a8f23b359571c0c1747ce6ce5705d0/vindex10}, description = {Hawking radiation and the Stefan-Boltzmann law: The effective radius of the black-hole quantum atmosphere}, interhash = {e9944987a698b585db2f5f77e5be3cb2}, intrahash = {d0a8f23b359571c0c1747ce6ce5705d0}, keywords = {black_holes gr}, note = {cite arxiv:1607.02510Comment: 6 pages}, timestamp = {2016-07-12T20:20:17.000+0200}, title = {Hawking radiation and the Stefan-Boltzmann law: The effective radius of the black-hole quantum atmosphere}, url = {http://arxiv.org/abs/1607.02510}, year = 2016 }