Multicritical phase transitions in multiply rotating black holes

Abstract We show that multi-critical points in which more than three phases coalesce are present in multiply rotating Kerr-anti de Sitter black holes in d -dimensions. We explicitly present a quadruple point for a triply rotating black hole in d = 8 and a quintuple point for a quadruply rotating black hole in d = 10. The maximal number of distinct phases n is one larger than the maximal number of independent rotations, and we outline a method for obtaining the associated n -tuple point. Situations also exist where more than three phases merge at sub-maximal multi-critical points. Our results show that multi-critical points in black hole thermodynamics are more common than previously thought, with systems potentially supporting many phases as long as a sufficient number of thermodynamic variables are present.