Dynamics of semi-classical black holes and the information loss problem

Abstract

In this thesis, the author studies the information loss problem using semi-classical black holes. If a black hole loses information after evaporation, it will imply the violation of unitarity and predictability. Therefore, to understand the nature of the Theory of Everything and to reconcile the quantum theory and gravitation, we need to understand the problem of the information loss. If we assume that there exists a unitary theory of quantum gravity as a working hypothesis, the area of a black hole is proportional to the statistical entropy of the black hole, and there is an observer who can see information from Hawking radiation, then it is inevitable to accept black hole complementarity. However, if there is an observer who can see both information of inside and outside, i.e., if the duplication experiment is possible, then black hole complementarity will be violated. A duplication experiment and other thought experiments can be investigated by semi-classical backgrounds. In this thesis, we focus on three subjects: gravitational objects of Einstein gravity with renormalized energy-momentum tensors, gravitational objects of modified theories of gravity, and initial conditions which can be prepared by quantum tunneling. To study such subjects, we use the following techniques: traditional analytic approaches, numerical approaches using the double-null formalism, and Euclidean analytic continuations. We study a possibility of a duplication experiment in a charged black hole and a regular black hole. Causal structures allow the possibility; but to regularize curvatures around the inner horizon, we require a sufficiently large number of massless fields which contribute to Hawking radiation. In fact, if we assume the large number, we can violate black hole complementarity even for neutral black holes. The required number of fields can be reduced to a reasonable amount; although we need a large number, if it is finite, the number may be allowed by a model of quantum gravity including string theory. This suggests that the area of the black hole may not imply the statistical entropy of the internal and physical degrees of freedom and there may be no observer who can read information via Hawking radiation. Also, we study a possibility of a formation of a bubble universe. The author used weaker assumptions than previous authors to obtain bubble universes. The Brans-Dicke theory can allow a false vacuum bubble as an instanton solution and such a theory may be allowed by quantum gravity including string theory. False vacuum bubbles will emit negative energy along the out-going direction and such negative energy can be used to obtain a bubble universe. Although we have to check whether these scenarios are possible in realistic quantum gravity, if it is possible, then it will strongly support a loss of information and a violation of unitarity at least in the ‘effective’ sense. These conclusions imply that, if there exists a unitary theory of quantum gravity or the Theory of Everything, we will observe a lose of information and a violation of unitarity in the ‘effective’ way.