A Note on Circular Geodesics and Phase Transitions of Black Holes

Abstract

The circular motion of charged test particles in the gravitational field of a Reissner-Nordström 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 $l=6Q$. 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.

arXiv commentv2:14 pages, 1 figure. Major changes in text and equations; added results; key results unchanged; v3: revised version, to appear in Physics Letters B

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