Numerical study of Hawking radiation photosphere formation around microscopic black holes - art. no. 063009

Heckler has recently argued that the Hawking radiation emitted from microsc opic black holes has sufficiently strong interactions above a certain criti cal temperature that it forms a photosphere, analogous to that of the Sun. In this case, the visible radiation is much cooler than the central tempera ture at the Schwarzschild radius, in contrast with the naive expectation fo r the observable spectrum. We investigate these ideas more quantitatively b y solving the Boltzmann equation using the test particle method. We confirm that at least two kinds of photospheres may form: a quark-gluon plasma for black holes of mass M(BH)less than or similar to 5 X 10(14) g and an elect ron-positron-photon plasma for M(BH)less than or similar to 2 X 10(12) g. T he QCD photosphere extends from the black hole horizon to a distance of 0.2 -4.0 fm for 10(9) g less than or similar to M(BH)less than or similar to 5 X 10(14) g, at which point quarks and gluons with average energy of order L ambda(QCD) hadronize. The QED photosphere starts at a distance of approxima tely 700 black hole radii and dissipates at about 400 fm, where the average energy of the emitted electrons, positrons and photons is inversely propor tional to the black hole temperature, and significantly higher than was fou nd by Heckler. The consequences of these photospheres for the cosmic diffus e gamma ray and antiproton backgrounds are discussed: bounds on the black h ole contribution to the density of the universe are slightly weakened. [S05 56-2821(99)03206-3].