How does a collapsing star look?
  Time evolution of an optical image of a pressureless star under gravitational
collapse is studied in the geometric optics approximation. The star surface is
assumed to emit radiation obeying Lambert's cosine law but with an arbitrary
spectral intensity in the comoving frame. We develop a formalism for predicting
observable quantities by photon counting and by radiometry, in particular,
spectral photon flux and spectral radiant flux. Then, this method is applied to
the two cases: One is monochromatic radiation, and the other is blackbody
radiation. The two kinds of spectral flux are calculated numerically for each
case. It is reconfirmed that the redshift factor remains finite and the star
becomes gradually invisible due to decay of the photon flux. We also develop an
approximate method to present analytic formulas that describe the late time
behavior. A possible connection of our study to observation of high-energy
neutrinos is briefly discussed.
