# Circular orbit of a test particle and phase transition of a black hole

## TL;DR

This paper explores how the radius of circular orbits of test particles around black holes can indicate thermodynamic phase transitions of the black holes, linking orbital dynamics to black hole thermodynamics.

## Contribution

It demonstrates that the phase transition information of a black hole can be inferred from the properties of test particles' circular orbits in its spacetime.

## Key findings

- Circular orbit radius reflects black hole phase transitions
- Test particle orbits encode thermodynamic information
- Orbit characteristics can indicate phase transition points

## Abstract

The radius of the circular orbit for the time-like or light-like test particle in a background of general spherically symmetric spacetime is viewed as a characterized quantity for the thermodynamic phase transition of the corresponding black hole. We generally show that the phase transition information of a black hole can be reflected by its surrounding particle's circular orbit.