QUANTUM FIELDS IN SCHWARZSCHILD–DE SITTER SPACE

In the No-Boundary Universe a primordial black hole is created from a constrained gravitational instanton. The black hole created is immersed in the de Sitter background with a positive cosmological constant. The constrained instanton is characterized not only by the external parameters, the mass parameter, charge and angular momentum, but also by one more internal parameter, the identification period in the imaginary time coordinate. Although the period has no effect on the black hole background, its inverse is the temperature of the no-boundary state of the perturbation modes perceived by an observer. By using the Bogoliubov transformation, we show that the perturbation modes of both scalar and spinor fields are in thermal equilibrium with the black hole background at the arbitrary temperature. However, for the two extreme cases, the de Sitter and the Nariai models, the no-boundary state remains pure.

REAL TUNNELING AND BLACK HOLE CREATION

We discuss the Hawking theory of quantum cosmology with regard to approximation at the lowest order of the Planck constant. At this level, the quantum scenario will be reduced to its classical evolutions in real and imaginary times. We restrict our attention to the so-called real tunneling case. It can be shown that, even at this level, there still exist some quantum effects, the classical field equation may not hold at the transition surface. One can introduce the concept of constrained gravitational instanton. It may play some important role in the scenario of black hole creation in the inflationary background at the Planckian era of the universe. From the constrained gravitational instanton, the real tunneling can occur through different ways. Consequently, it will lead to the creation of different parts of the black hole spacetime in the de Sitter background. The global aspects of the black hole creation are discussed.