Semiclassical and Quantum Black Holes and their Evaporation, de Sitter and Anti-de Sitter Regimes, Gravitational and String Phase Transitions

An effective string theory in physically relevant cosmological and black hole space times is reviewed. Explicit computations of the quantum string entropy, partition function and quantum string emission by black holes (Schwarzschild, rotating, charged, asymptotically flat, de Sitter dS and AdS space times) in the framework of effective string theory in curved backgrounds provide an amount of new quantum gravity results as: (i) gravitational phase transitions appear with a distinctive universal feature: a square root branch point singularity in any space time dimensions. This is of the type of the de Vega - Sanchez transition for the thermal self-gravitating gas of point particles. (ii) There are no phase transitions in AdS alone. (iii) For $dS$ background, upper bounds of the Hubble constant H are found, dictated by the quantum string phase transition.(iv) The Hawking temperature and the Hagedorn temperature are the same concept but in different (semiclassical and quantum) gravity regimes respectively. (v) The last stage of black hole evaporation is a microscopic string state with a finite string critical temperature which decays as usual quantum strings do in non-thermal pure quantum radiation (no information loss).(vi) New lower string bounds are given for the Kerr-Newman black hole angular momentum and charge, which are entirely different from the upper classical bounds. (vii) Semiclassical gravity states undergo a phase transition into quantum string states of the same system, these states are duals of each other in the precise sense of the usual classical-quantum (wave-particle) duality, which is universal irrespective of any symmetry or isommetry of the space-time and of the number or the kind of space-time dimensions.

Microcanonical model for a gaz of evaporating black holes and strings, scattering amplitudes and mass spectrum

We study the system formed by a gaz of black holes and strings within a microcanonical formulation. We derive the microcanonical content of the system: entropy, equation of state, number of components N, temperature T and specific heat. The pressure and the specific heat are negative reflecting the gravitational unstability and a non-homogeneous configuration. The asymptotic behaviour of the temperature for large masses emerges as the Hawking temperature of the system (classical or semiclassical phase) in which the classical black hole behaviour dominates, while for small masses (quantum black hole or string behavior) the temperature becomes the string temperature which emerges as the critical temperature of the system. At low masses, a phase transition takes place showing the passage from the classical (black hole) to quantum (string) behaviour. Within a microcanonical field theory formulation, the propagator describing the string-particle-black hole system is derived and from it the interacting four point scattering amplitude of the system is obtained. For high masses it behaves asymptotically as the degeneracy of states of the system (ie duality or crossing symmetry). The microcanonical propagator and partition function are derived from a (Nambu-Goto) formulation of the N-extended objects and the mass spectrum of the black-hole-string system is obtained: for small masses (quantum behaviour) these yield the usual pure string scattering amplitude and string-particle spectrum M_napprox sqrt{n}; for growing mass it pass for all the intermediate states up to the pure black hole behaviour. The different black hole behaviours according to the different mass ranges: classical, semiclassical and quantum or string behaviours are present in the model.