The Last Eight Minutes of a Primordial Black Hole

Abstract

About eight minutes before a black hole expires it has a decreasing mass of 10^{10} g, an increasing temperature of 1 TeV, and an increasing luminosity of 7x10^{27} erg/s. I show that such a black hole is surrounded by a quasi-stationary shell of matter undergoing radial hydrodynamic expansion. The inner radius of this shell is bounded by ten times the Schwarzschild radius of 1.6x10^{-5} fm and has a temperature about one-tenth that of the black hole. The outer radius, as defined by the photosphere, is about 1000 fm, has a local temperature of 100 keV, and is moving with a Lorentz gamma factor of 10^7. Most of the emitted radiation is in photons with small amounts in gravitons and neutrinos. I calculate the instantaneous photon spectrum and then integrate it over the last eight minutes to obtain the energy distribution dN_{gamma}/dE = 4πm_{P}^2/15E^3 for E > several TeV .