The Last Eight Minutes of a Primordial Black Hole
Kapusta, Joseph
Original · EN
About eight minutes before a black hole expires it has a decreasing mass of 10¹⁰ g, an increasing temperature of 1 TeV, and an increasing luminosity of 7x10²⁷ 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 10⁷. 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 dNgamma/dE = 4πmₚ²/15E³ for E > several TeV.
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