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Masterarbeit Böhm
Fichas del conjunto (9)
- 1Cauchy surfaceAre spacelike surfaces, whose connection to an arbitrary point of M is given by
a causal curve
Is any subset of space-time which is intersected by every inextensible, non-spacelike (i.e. causal) curve exactly once. - 2Globally hyperbolic spacetimeA spacetime consisting of Cauchy surfaces is called globally hyperbolic
- 3Causal cuve and spacelike curveA causal curve is a curve that is either timelike or lightlike - that is the norm of
the tangent vector to this curve is everywhere smaller than zero or zero respectively. A curve
that is not causal is called spacelike. - 4Theorem by GerochStates that any globally hyperbolic spacetime M is
necessarily of the topology M \(\cong\) R x \(\sigma\), where the three-dimensional manifold \(\sigma\) is fxed and
of arbitrary topology - 5EmbeddingA map \(\Psi : M \rightarrow N \) is an embedding if \(\Psi\) is an immersion and \( \Psi(M)\cong_{top} N\)
- 6ImmersionA smooth map \(\Psi : M \rightarrow R^n \) is called an immersion of M in R^n if the derivative of the map ( =pushforward) is injective at any point p in M.
- 7Gowdy model-Is a special cos-
mological model in general relativity, which is equipped with certain symmetries
-is of special interest for quantum gravity since it is easier to quantize than the full theory and therefore allows to test the methods of quantum gravity on a simple model. - 8Einstein-Hilbert actionmetric signature: (-+++)
\(S = {1 \over 2\kappa} \int R \sqrt{-g} \, \mathrm{d}^4x \;, \)
Integration over the manifold describing our spacetime - 9space-like surfacea collection of points such that every pair is space-like separated
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- Fichas sobre Masterarbeit Böhm, creado por andreas.leithere el 12/11/2015.
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