Reddening Behaviors of Galaxies in the SDSS Photometric System

We analyze the behaviors of reddening vectors in the SDSS photometric system for galaxies of different morphologies, ages, and redshifts. As seen in other photometric systems, the dependence of reddening on the spectral energy distribution (SED) and the nonlinearity of reddening are likewise non-negligible for the SDSS system if extinction is significant (~> 1 mag). These behaviors are most significant for the g filter, which has the largest bandwidth-to-central wavelength ratio among SDSS filters. The SDSS colors involving adjacent filters show greater SED-dependence and nonlinearity. A procedure for calculating the correct amount of extinction from an observed color excess is provided. The relative extinctions between (i.e., the extinction law for) SDSS filters given by Schlegel et al., which were calculated with an older version of filter response functions, would underestimate the amount of extinction in most cases by ~5 to 10 % (maximum ~20 %). We recommend A/A_{5500} values of 1.574, 1.191, 0.876, 0.671 & 0.486 for the u, g, r, i, & z filters, respectively, as a representative extinction law for the SDSS galaxies with a small extinction (i.e., for cases where the nonlinearity and SED-dependence of the reddening is not important). The dependence of reddening on redshift at low extinction is the largest for colors involving the g filter as well, which is due to the Balmer break.Comment: Published in PASP, 119, 1449 (Dec. 2007

Phase transition between non-extremal and extremal Reissner-Nordstr\"om black holes

We discuss the phase transition between non-extremal and extremal Reissner-Nordstr\"om black holes. This transition is considered as the $T \to 0$ limit of the transition between the non-extremal and near-extremal black holes. We show that an evaporating process from non-extremal black hole to extremal one is possible to occur, but its reverse process is not possible to occur because of the presence of the maximum temperature. Furthermore, it is shown that the Hawking-Page phase transition between small and large black holes unlikely occurs in the AdS Reissner-Nordstr\"om black holes.Comment: 12 pages, 6 figures, version to appear in MPL