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Deeg, Dorothea (2006): Quantum Aspects of Black Holes. Dissertation, LMU München: Faculty of Physics
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Abstract

In this thesis we study two quantum aspects of black holes, their entropy and the Hawking effect. First, we present a model for the statistical interpretation of black hole entropy and show that this entropy emerges as a result of missing information about the exact state of the matter from which the black hole was formed. We demonstrate that this idea can be applied to black holes made from both ultra-relativistic and nonrelativistic particles. In the second part we focus our attention on several features of black hole evaporation. We discuss the dependence of the Hawking radiation on the vacuum definition of different observers. It becomes evident that in certain cases the choice of observer has an influence on the particle spectrum. In particular, we study the meaning of the Kruskal vacuum on the horizon. After that we determine the Hawking flux for nonstationary black holes. We find approximate coordinates which are regular on the time dependent horizon and calculate the particle density measured by an observer at infinity. Finally, we derive the response of a particle detector in curved background. In our approach we use the Unruh detector to quantify the spectrum of radiation seen by general observers in Minkowski, Schwarzschild and Vaidya space-times. We find that an arbitrarily accelerated detector in flat space-time registers a particle flux with a temperature proportional to a time dependent acceleration parameter. A detector moving in Schwarzschild space-time will register a predominantly thermal spectrum with the exact temperature depending on the observer's trajectory. If the detector is located at constant distance from the black hole it measures a shifted temperature which diverges on the horizon. On the other hand, a detector in free fall towards the black hole does not register a thermal particle flux when it crosses the horizon. In this framework corrections to the temperature measured by a detector moving in Vaidya space-time are obtained as well. We argue that our result also clarifies the role of horizons in black hole radiation.