A Note on Circular Geodesics and Phase Transitions of Black Holes

TL;DR

This paper explores the circular geodesics of charged particles around Reissner-Nordström-AdS black holes and links specific orbital features to black hole phase transitions, suggesting a deep connection between black hole thermodynamics and particle motion.

Contribution

It introduces a classification of circular orbits in Reissner-Nordström-AdS spacetime and connects special orbital conditions to black hole phase transition points.

Findings

Identification of special orbit radii at phase transition points

Connection between thermodynamic phase transitions and geodesic structure

Potential implications for black holes in flat spacetime in a box

Abstract

The circular motion of charged test particles in the gravitational field of a Reissner-Nordstr\"{o}m black hole in Anti de Sitter space-time is investigated, using a set of independent parameters, such as charge Q, mass M and cosmological constant $\Lambda= -3/l^2$ of the space-time, and charge to mass ratio $\epsilon=q/m$ of the test particles. Classification of different spatial regions where circular motion is allowed, is presented, showing in particular, the presence of orbits at special limiting values, $M=4/\sqrt{6} Q$ and $l=6 Q$. Thermodynamically, these values are known to occur when the black hole is on the verge of a second order phase transition, there by, giving an interesting connection between thermodynamics and geodesics of black holes. We also comment on the possibility of such a connection for black holes in flat spacetime in a box.