Abstract.The problem of communication between observers in the vicinity of a black hole in a Schwarzschild metric is considered. The classic example of an infalling observer Alice and a static distant mothership MS is extended to include a second infalling observer Bob, who follows Alice in falling towards the event horizon. Kruskal coordinates are introduced to analyze this situation, and the pedagogic value of introducing this alternative coordinate system is demonstrated by their ability to provide a graphically based solution and illustration to this problem. The counterintuitive result that is obtained, which will be of interest to those studying general relativity at an introductory level at final year undergraduate or at graduate level, is that Bob appears to reach a ghostly image of Alice at the event horizon.
Effective theories are non-local at the scale of the eliminated heavy
particles modes. The gradient expansion which represents such non-locality must
be truncated to have treatable models. This step leads to the proliferation of
the degrees of freedom which renders the identification of the states of the
effective theory nontrivial. Furthermore it generates non-definite metric in
the Fock space which in turn endangers the unitarity of the effective theory.
It is shown that imposing a generalized KMS boundary conditions for the new
degrees of freedom leads to reflection positivity for a wide class of Euclidean
effective theories, thereby these lead to acceptable theories when extended to
real time.Comment: 8 pages, no figures, to appear in Physical Review
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