# Upper bound on the radii of regular ultra-compact star photonspheres

## TL;DR

This paper establishes an upper bound on the radii of photonspheres in regular asymptotically flat compact stars, considering various gravity theories and matter field effects, with implications for understanding ultra-compact objects.

## Contribution

It provides a general proof of an upper bound on photonsphere radii for regular compact stars, including cases with matter backreaction and different gravity theories.

## Key findings

- Photonsphere radius has an upper bound related to ADM mass.
- Stronger bounds are derived for stars with negative isotropic trace.
- Results apply to a broad class of regular ultra-compact stars.

## Abstract

We investigate the photonsphere in the background of regular asymptotically flat compact stars. The analysis includes the general hairy compact star considering the matter fields' backreaction on the metric in various gravity theories. We prove that the photonsphere of the compact star has an upper bound expressed in terms of the ADM mass of the spacetime. In the case of negative isotropic trace, a stronger upper bound can be obtained.