On the Black Hole/black Ring Transition

We study the possibility of a phase transition in D = 5 between a rotating black hole and the "black ring" solution of Emparan and Reall. We address the issue of stability of these spacetimes and its relation to thermodynamics by using the so-called "Poincaré method" of stability. We also use the geometry of the thermodynamic state space ("Ruppeiner geometry") to gain information about the critical point and nature of the transition. Finally, we are able to compute the appropriate critical exponents and verify that the scaling laws are satisfied.