# How does a collapsing star look?

## TL;DR

This paper models the optical appearance of a collapsing star over time using geometric optics, analyzing spectral flux and redshift effects, and discusses potential observational implications including neutrino detection.

## Contribution

It develops a formalism for predicting observable radiation from collapsing stars, including spectral flux calculations for monochromatic and blackbody emissions, with analytic late-time behavior formulas.

## Key findings

- Photon flux diminishes as the star collapses, making it gradually invisible.
- Redshift factor remains finite during collapse.
- Analytic formulas describe late-time spectral flux behavior.

## Abstract

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.