Seeing through a nearly black star

TL;DR

This paper explores how a nearly black, semi-transparent star appears to an outside observer, revealing a transition from a three-dimensional object to a two-dimensional membrane as it approaches black hole formation, with implications for entropy laws.

Contribution

It demonstrates that a nearly black star appears as a two-dimensional membrane to external observers measuring certain distances, and discusses the implications for the entropy area law during collapse.

Findings

Perceived distance between shell surfaces approaches zero near Schwarzschild radius.

Interior emitters' images squeeze around the shell surfaces in certain distance measures.

Depth information inside the star can still be obtained via radar or luminosity distances.

Abstract

A nearly black, gravitationally intense star of semi-transparent, spherical, massive shell containing a few pointlike light sources inside would be perceived not like a three-dimensional ball for a localized observer outside the shell in terms of the affine or binocular distance. As the radius of the spherical shell approaches the Schwarzschild radius, the perceived distance between the front and rear surfaces of the shell would go to zero, while the images of most of the interior emitters would squeeze around the shell surfaces in terms of the affine or binocular distance. So, the Schwarzschild black hole formed from the star would be thought of as a two-dimensional membrane for the observers who can only measure the binocular distance and/or affine distance. However, the depth information of a point source inside the nearly black star can still be resolved in terms of the radar or luminosity distance, which needs the knowledge about the radar signals or standard candles sent in earlier by the observer outside the star. This suggests that at late times of gravitational collapse the area law of the entropy would dominate over the volume law for outside observers due to the loss of the knowledge about the ingoing probes earlier.