On the formation of a Hawking-radiation photosphere around microscopic black holes

We show that once a black hole surpasses some critical temperature $T_{crit}$, the emitted Hawking radiation interacts with itself and forms a nearly thermal photosphere. Using QED, we show that the dominant interactions are bremsstrahlung and electron-photon pair production, and we estimate $T_{crit} \sim m_{e}/\alpha^{5/2}$, which when calculated more precisely is found to be $T_{crit} \approx$45 GeV. The formation of the photosphere is purely a particle physics effect, and not a general relativistic effect, since the the photosphere forms roughly $\alpha^{-4}$ Schwarzschild radii away from the black hole. The temperature $T$ of the photosphere decreases with distance from the black hole, and the outer surface is determined by the constraint $T\sim m_{e}$ (for the QED case), since this is the point at which electrons and positrons annihilate, and the remaining photons free stream to infinity. Observational consequences are discussed, and it is found that, although the QED photosphere will not affect the Page-Hawking limits on primordial black holes, which is most important for 100MeV black holes, the inclusion of QCD interactions may significantly effect this limit, since for QCD we estimate $T_{crit}\sim \Lambda_{QCD}$. The photosphere greatly reduces possibility of observing individual black holes with temperatures greater than $T_{crit}$, since the high energy particles emitted from the black hole are processed through the photosphere to a lower energy, where the gamma ray background is much higher. The temperature of the plasma in the photosphere can be extremely high, and this offers interesting possibilities for processes such as symmetry restoration.Comment: Latex, 16 pages, 3 postscript figures, submitted to PRD. Also available at http://fnas08.fnal.gov

Chiral Symmetry Breaking in Quenched Massive Strong-Coupling QED4_4

We present results from a study of subtractive renormalization of the fermion propagator Dyson-Schwinger equation (DSE) in massive strong-coupling quenched QED$_4$. Results are compared for three different fermion-photon proper vertex {\it Ans\"{a}tze\/}: bare $\gamma^\mu$, minimal Ball-Chiu, and Curtis-Pennington. The procedure is straightforward to implement and numerically stable. This is the first study in which this technique is used and it should prove useful in future DSE studies, whenever renormalization is required in numerical work.Comment: REVTEX 3.0, 15 pages plus 7 uuencoded PostScript figure

Est locus uni cuique suus: City and Status in Horace’s Satires 1.8 and 1.9

This is the published version

Relativistic Viscous Fluid Description of Microscopic Black Hole Wind

Microscopic black holes explode with their temperature varying inversely as their mass. Such explosions would lead to the highest temperatures in the present universe, all the way to the Planck energy. Whether or not a quasi-stationary shell of matter undergoing radial hydrodynamic expansion surrounds such black holes is been controversial. In this paper relativistic viscous fluid equations are applied to the problem. It is shown that a self-consistent picture emerges of a fluid just marginally kept in local thermal equilibrium; viscosity is a crucial element of the dynamics.Comment: 11 pages, revte

Numerical Study of Hawking Radiation Photosphere Formation around Microscopic Black Holes

Heckler has recently argued that the Hawking radiation emitted from microscopic black holes has sufficiently strong interactions above a certain critical temperature that it forms a photosphere, analogous to that of the sun. In this case, the visible radiation is much cooler than the central temperature at the Schwarzschild radius, in contrast to the naive expectation for the observable spectrum. We investigate these ideas more quantitatively by 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} < 5 times 10^{14} g and an electron-positron-photon plasma for M_{BH} < 2 times 10^{12} g. The QCD photosphere extends from the black hole horizon to a distance of 0.2--4.0 fm for 10^9 g < M_{BH} < 5 10^{14} g, at which point quarks and gluons with average energy of order \Lambda_{QCD} hadronize. The QED photosphere starts at a distance of approximately 700 black hole radii and dissipates at about 400 fm, where the average energy of the emitted electrons, positrons and photons is inversely proportional to the black hole temperature, and significantly higher than was found by Heckler. The consequences of these photospheres for the cosmic diffuse gamma ray and antiproton backgrounds are discussed: bounds on the black hole contribution to the density of the universe are slightly weakened.Comment: 25 pages, Latex, 33 figures ; some incorrect references fixe

Dynamical Left-Right Symmetry Breaking

We study a left--right symmetric model which contains only elementary gauge boson and fermion fields and no scalars. The phenomenologically required symmetry breaking emerges dynamically leading to a composite Higgs sector with a renormalizable effective Lagrangian. We discuss the pattern of symmetry breaking and phenomenological consequences of this scenario. It is shown that a viable top quark mass can be achieved for the ratio of the VEVs of the bi--doublet $\tan\beta\equiv\kappa/\kappa'$ =~ 1.3--4. For a theoretically plausible choice of the parameters the right--handed scale can be as low as $\sim 20 TeV$; in this case one expects several intermediate and low--scale scalars in addition to the \SM Higgs boson. These may lead to observable lepton flavour violation effects including $\mu\to e\gamma$ decay with the rate close to its present experimental upper bound.Comment: 51 pages, LaTeX and uuencoded, packed Postscript figures. The complete paper, including figures, is also available via WWW at http://www.cip.physik.tu-muenchen.de/tumphy/d/T30d/PAPERS/ TUM-HEP-222-95.ps.g