An analytic solution is presented for the thermal radiation spectrum from a star undergoing catastrophic collapse to a black hole. The matter distribution and gravitational field are modeled by the Oppenheimer-Snyder solution for spherical, homogeneous, dust-ball collapse. The radiation flux emitted during the implosion is calculated assuming the star is initially subjected to a dynamically small, isothermal temperature perturbation. The flux is derived in the diffusion approximation for a constant opacity source and is determined for distant, as well as comoving observers. Both a Newtonian and general-relativistic analysis are performed. As seen by a distant observer, the intensity at late times appears as a constant blackbody originating from a shrinking annular region about the black hole. The corresponding effective temperature is a simple function of the initial stellar parameters. The total luminosity is constant to a comoving observer at late times, but decays exponentially according to a distant observer. Though highly idealized, our exact solution may serve as a useful benchmark for testing fully relativistic, radiation-transport codes now under construction to handle more complicated collapse scenarios.
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)