Radiation from Stellar Collapse to a Black Hole

Abstract

Calculating the radiation from stellar collapse to a black hole requires a relativistic treatment of the gravitational field, hydrodynamical flow, and radiative transport. We adopt a model for a collapsing star in general relativity that is sufficiently simple that we can focus on the radiative transport and treat it essentially without approximation. The matter and gravitational field are described by the Oppenheimer- Snyder solution for the collapse of a spherical, homogeneous dust ball. Transport is calculated numerically by solving the radiation moment equations in conjunction with the complete angle-dependent Boltzmann equation for the intensity. The intensity can describe photons, neutrinos, or any other form of radiation. Thermal emission and absorption as well as coherent isotropic scattering sources are included. All opacities are chosen to be constant and gray. We present analytic solutions to our transport equations in both optically thick and transparent regimes and compare them to our numerical results. We also use our model to evaluate simplifications like the diffusion approximation in a relativistic setting. Our simple treatment can be used to explore a wide variety of stellar parameters and to test more sophisticated relativistic collapse codes containing radiation transport For any given choice of parameters, our model can determine the comoving radiation field in a collapsing star in a few minutes on a typical workstation.