Dynamical origin of black-hole radiance

Abstract

An explanation of the thermal quantum radiance of black holes discovered by Hawking is offered in terms of a black-hole metric undergoing quantum zero-point fluctuations of zero mean in its gravitational quasinormal modes. It is shown that such zero-temperature fluctuations, governed by the uncertainty principle, lead to the formation of a quantum ergosphere that enables matter of all species to tunnel out of the hole. The results confirm that a black hole cannot be in equilibrium at zero temperature. A dynamical temperature is calculated by equating the mean irreducible mass associated with the quantum ergosphere to the mean thermal energy of a quantum oscillator with the lowest quasinormal frequency. The result agrees with the Hawking temperature to within two per cent. The nature of the dynamical equilibrium and the higher modes are discussed, and it is calculated that the thermal excitations of the resonant modes have the canonical distribution to within several per cent. A calculation of the black-hole entropy using the statistical mechanics of the quasinormal modes yields a value $\mathrm{}\left(0.27654\right)\mathrm{}{\hslash }^{-1\mathrm{}}\left(16\mathrm{}\pi M^2\right)$, which is near the value usually assumed, $\mathrm{}\left(0.25\right)\mathrm{}{\hslash }^{-1\mathrm{}}\left(16\mathrm{}\pi M^2\right)$. Characteristic fluctuation scales are derived. The rms energy fluctuation of the physical ("dressed") event horizon is about ${10}^{17}$ GeV, independent of $M$. The physical metric fluctuations near the hole are of order unity when the hole has mass ≈ (0.15) (Planck mass) ≈ 1.8×${10}^{18}$ GeV.