Abstract
We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates of the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a discrete spectrum, definitely non-thermal. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area computed using loop quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov discrete spectrum, but — effectively — a continuum spectrum, consistent with Hawking's result. The Bekenstein-Mukhanov argument for the discreteness of the specrum is therefore likely to be an artifact of the ansatz, rather than a robust result (at least in its present kinematical version). The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.
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This essay received the second award from the Gravity Research Foundation, 1996—Ed.
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Barreira, M., Carfora, M. & Rovelli, C. Physics with nonperturbative quantum gravity: Radiation from a quantum black hole. Gen Relat Gravit 28, 1293–1299 (1996). https://doi.org/10.1007/BF02109521
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DOI: https://doi.org/10.1007/BF02109521