Institut für Quantenphysik
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Gödel's Universe
An interesting solution of Einstein's field equations was found by Kurt Gödel in 1949. The so-called Gödel Universe describes a homogeneous rotating universe in which closed timelike world lines exist. Traveling along such a world line allows an observer the mind-boggling journey into his own past. In our research we address the question how an observer located in such a universe would perceive his surrounding visually. This is particularly interesting since the Gödel universe provides a couple of compelling optical effects such as the existence of an optical horizon or the refocusing of light. In order to visualize scenarios in Gödel's universe, we use an adapted version of ray tracing which requires detailed knowledge of the light propagation in this space-time. In addition, we are interested in the time evolution of scalar fields at the brink of causality. When we restrict the wave dynamics in Gödel's Universe to a sufficiently small region that contains no closed timelike or null curves, and require Dirichlet boundary conditions for the scalar fields, the Cauchy initial-value problem becomes well-posed and we can expect a unique solution of the scalar wave equation. As a result, we find characteristic revivals of an arbitrary initial wave packet. The corresponding revival times are semiclassically related to those of a massive point particle traveling periodically along its geodesic. The ultimate question we hereby address is the search for specific signatures in the behavior of the scalar field when the restricted spacetime region approaches the critical size at which a violation of causality becomes possible.
Publications
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