Quantum-Gravity Fluctuations and the Black-Hole Temperature

TL;DR

This paper explores how quantum gravity fluctuations lead to a discrete black-hole radiation spectrum with an effective temperature that matches Hawking's semi-classical temperature, bridging quantum and classical descriptions.

Contribution

It demonstrates that zero-point quantum-gravity fluctuations can produce a black-hole temperature consistent with Hawking's prediction, reconciling discrete and continuous spectra.

Findings

Discrete black-hole radiation temperature matches Hawking temperature

Quantum fluctuations relate to black-hole resonances

Effective temperature derived from quantum fluctuations aligns with semi-classical results

Abstract

Bekenstein has put forward the idea that, in a quantum theory of gravity, a black hole should have a discrete energy spectrum with concomitant discrete line emission. The quantized black-hole radiation spectrum is expected to be very different from Hawking's semi-classical prediction of a thermal black-hole radiation spectrum. One naturally wonders: Is it possible to reconcile the {\it discrete} quantum spectrum suggested by Bekenstein with the {\it continuous} semi-classical spectrum suggested by Hawking ? In order to address this fundamental question, in this essay we shall consider the zero-point quantum-gravity fluctuations of the black-hole spacetime. In a quantum theory of gravity, these spacetime fluctuations are closely related to the characteristic gravitational resonances of the corresponding black-hole spacetime. Assuming that the energy of the black-hole radiation stems from these zero-point quantum-gravity fluctuations of the black-hole spacetime, we derive the effective temperature of the quantized black-hole radiation spectrum. Remarkably, it is shown that this characteristic temperature of the {\it discrete} (quantized) black-hole radiation agrees with the well-known Hawking temperature of the {\it continuous} (semi-classical) black-hole spectrum.