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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 Λ = −3/l 2 of the space-time, and charge to mass ratio = 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/ √ 6Q 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. 1 chandrasekhar@iitbbs.ac.in 2 sm32@iitbbs.ac.in 1 arXiv:1805.05088v3 [hep-th]

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