Self-gravitating phase transitions: Point particles, black holes and strings

We compute the quantum string entropy S-s (m, j) of the microscopic string states of mass in and spin j in two physically relevant backgrounds: Kerr (rotating) black holes and de Sitter (dS) space-time. We find a new formula for the quantum gravitational entropy S-sem(M, J), as a function of the usual Bekenstein-Hawking entropy S-sem((0))(M, J). We compute the quantum string emission by a black hole in de Sitter space-time (bhdS). In all the following cases: (i) strings with the highest spin, and (ii) in dS space-time, (iii) quantum rotating black holes, (iv) quantum dS regime, (v) late bhdS evaporation, we find a new gravitational phase transition with a common distinctive universal feature: a square root branch point singularity in any space-time dimensions. This is the same behavior as for the thermal self-gravitating gas of point particles (de Vega-Sanchez transition), thus describing a new universality class.