Quantum Aspects of Black Holes

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.