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 m 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. To cite this article: N.G. Sanchez, C. R. Physique 7 (2006).