Quantum Spectrum Of Stationary Axisymmetric Einstein-Maxwell Dilaton-Axion Black Hole

Superstring theory springing up in recent years is still the only known self-consistent theory which can quantize the gravity and unify the gravity, the electromagnetic interaction, the weak interaction and the strong interaction. This theory can explain the cosmic genesis and evolution, and figure out the problems of modern physics. In terms of the dilaton spacetimes in string theory, black hole has qualitatively different properties from those appearing in general relativity because of the apearance of dilaton. So there have been many investigations concerning the spacetimes of dilaton black hole. It is by now well known that one of the outstandingly unsolved questions in gravitational theory is the microscopic origin of black-hole thermodynamic entropy. In all likelihood, this question can only be addressed in the context of quantum theory of gravity . Nonetheless there are still some fundament issues that can be investigated even the absence of the full-developed quantum theory, say, what is the quantum spectrum of the black hole. Especially, people realy have had a little knowledge of black hole's spectrum in candidate theories of quantum gravity.In this paper our main purpose is to extend the research of the horizon area spectrum into the case of stationary axisymmetric Einstein-Maxwell Dilaton-Axion (EMDA) spacetime. The horizon area spectrum of the stationary axisymmetric EMDA black hole is studied by using Gour-Medved's method, which essentially belongs to the frame of reduced phase space. A remarkable feature of this eigenvalue spectrum is that vacuum fluctuation prevents the extremal black holes from the quantum spectrum due to the zero-point term. This result can best be viewed as a quantum black hole version of the third law of thermodynamics. As a result of this area spectrum, the spectrum of M is discrete, bounded below, and can be made positive. Prom the physical point of view, the semiboundedness and positivity of the spectrum are very satisfying results: The semi-boundedness of the spectrum implies that one cannot extract an infinite amount of energy from the system, whereas the positivity of the spectrum is in agreement with the well-known positive-energy theorems of general relativity. Roughly speaking, the ADM energy of the stationary axisymmetric EMDA spacetime is always positive or zero. Moreover, it is found that the quantized area operator can be expressed in terms of two quantum num-bers, i.e., A = 8tt^(| + n + l), where n and I are strictly non-negative integers and related respectively to the mass and angular momentum. The result shows that there is a qualitatively different property between the quantum spectrum of the EMDA black hole which obtained from string theory and the one of the Kerr-Newman black hole which obtained from general relativity, although both they are characterized by mass, angular momentum and charge. In fact, in the case of the extremal stationary axisymmetric EMDA black hole, Jd = y M2 — |￡ is a function of the black hole mass and charge, but the horizon area is just the compound function of this function, which yields the intriguing feature of this black hole derived from string theory.