  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.
