The Complex Quantum-State of Black-Hole and Thermostatistics.

Abstract

In this paper the quantum aspects are described in-detail with the help of a new type of energy source called latent energy group SU(6) of the super unified theory of SU(11). The thermodynamics of general self gravitating systems created by the energy group SU(6) and some related topics such as complex space-time (i.e. Pseudo-Space-Time) are also briefly discussed. The thermodynamic connection is based on Hawking celebrated application of quantum theory to Black-Hole. We know that macroscopic systems have definite and precise energies, subject to definite conservation principle. In this paper the generalized theory of black-hole is examined in-detail. We study the quantum state of black-hole. We consider our universe begins through the symmetry breaking of the super unified theory with gauss group SU(11) (  SU(6)  SU(5)  U(1)) from 7-dimensionsl space-time. The subgroup SU(6) has been interpreted as a new type of energy source other than SU(5) (SU(5)  SU (3)  SU(2)  U(1), where SU(3), the strong energy group, SU(2) the weak-energy group and U(1), the electro-dynamics). The energy group SU(6) are responsible for the situation of the so-called black-hole and U(1), also for the creation of Schwarzschild mass 'M' and angular momentum 'J', as U(1) are responsible for the creation of electric charge 'e' ( where M & J- depends on 'e' as shown in this paper ). We consider the line element proposed by the quantum-vacuum Kantowski-Sachs universe without cosmological constant. We also consider the scale factor b(= iR) of the metric to be imaginary and the other a( = R) is real, of the Kantowski-Sachs quantum-state with complex space- time. Solving the metric tensors we get the energy tensors in the 10(= 4+6) dimensional spacetime under the exchange RI ↔ R. We think from 10-dimensional to 7-dimensional stage, the situation of primordial black-hole formed by the energy group SU(11). The fact is obviously defined within 10- dimensional to7-dimensional flat universe and then the black-hole formed within 7-dimensional to 4- dimensional closed universe through the symmetry breaking of the energy group SU(11), the negative pressure by is define the matter energy density and is define the latent energy density. At the early stage The universe then begins its journey through the phase transition system.