Exact solutions for null fluid collapse

Exact nonstatic spherically symmetric solutions of the Einstein equations for a null fluid source with pressure P and density ρ related by P=k${\mathrm{\rho }}^{\mathit{a}}$ are given. The a=1 metrics are asymptotically flat for 1/2<k≤1 and cosmological for 0<k<1/2. The k=1 metric is the known charged Vaidya solution. In general the metrics have multiple apparent horizons. In the long time limit, the asymptotically flat metrics are hairy black hole solutions that ‘‘fall between’’ the Schwarzschild and Reissner-Nordström metrics. © 1996 The American Physical Society.