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

Abstract

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 (0) sem (M, J). We compute the quantum string emission by a black hole in de Sitter space-time (bhdS). In all these 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.Nous calculons l'entropie S s (m, j) desétats microscopiques de masse m et spin j des cordes quantiques dans deux espaces-temps physiquement relevants: Le trou noir en rotation (de Kerr) et l'espace-temps de de Sitter (dS). Nous trouvons une nouvelle formule pour l'entropie gravitationnelle quantique S sem (M, J) comme fonction de l'entropie de Bekenstein-Hawking S (0) sem (M). Nous calculons l'émission quantique des cordes par un trou noir avec constante cosmologique (bhdS). Dans tous ces cas: (i) cordes avec le spin maximal, et (ii) dans l'espace-time de dS, (iii) trous noirs de grand moment angulaire, (iv) regime quantique de dS, (v) dernièreétape d'évaporation bhdS, nous trouvons une nouvelle transition de phase avec la même caractéristique distinctive universelle : un point de ramification racine carréeà la transition, pour toute dimension de l'espace-temps. C'est le même comportement que pour le gaz auto gravitant de particules ponctuelles (transition de de Vega-Sanchez), définissant ainsi une nouvelle classe d'universalité.

Semiclassical and Quantum Black Holes and Their Evaporation, De Sitter and Anti-De Sitter Regimes, Gravitational and String Phase Transitions

“…The latter string transitions show a logarithmic square root branch point type of singularity for the entropy (and a pole singularity for the specific heat); this behavior is similar to the one found for a thermal self-gravitating gas of non relativistic particles (de Vega -Sánchez transition) [34], [35], [36], [65]. This string behavior is universal [29], [66]i.e. it holds in any number of dimensions, and its origin is gravitational interaction in the presence of temperature (as Jean's instability at finite temperature but with a more complex structure).…”

“…4 : the signature of this transition is the square root branch point behavior at the critical mass (temperature) analogous to the thermal self-gravitating gas phase transition of point particles [34]- [36], [65] and to the string gas in dS space. This behavior is universal, and happens in any number of space-time dimensions [29], [66] . We have already seen the same feature for the extremal Kerr black hole (high angular momentum J → M 2 G/c, extremal transition).…”