Superfluid Black Holes

We present what we believe is the first example of a lambda-line phase transition in black hole thermodynamics. This is a line of (continuous) second order phase transitions which in the case of liquid He-4 marks the onset of superfluidity. The phase transition occurs for a class of asymptotically anti-de Sitter hairy black holes in Lovelock gravity where a real scalar field is conformally coupled to gravity. We discuss the origin of this phase transition and outline the circumstances under which it (or generalizations of it) could occur.