GLOBAL LORENTZIAN GEOMETRY

By J. Grant. 2009

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On smooth time functions (2011, background): “Notice also that this requirements rules out compact space–time since it can be proved, see [2] Proposition 3.10, that compactness and causality are incompatible.”
The causal hierarchy of spacetimes (2006, methodology): “…. . . . . . . . . . . . . . . . . . . . . . . 12 2.6 Lightlike geodesics and conjugate events . . . . . . . . . . . . . . . . . . . . . . . . 14 3 The causal hierarchy 18 3.1 Non-totally vicious spacetimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 3.2 Chronological…”
Coherent Lagrangian vortices: the black holes of turbulence (2013, background): “Thus, (Uλ, gλ) can be viewed as a two-dimensional Lorentzian manifold (Beem et al. 1996), or in the language of general relativity, a two-dimensional spacetime.”
Algebraic QFT in Curved Spacetime and Quasifree Hadamard States: An Introduction (2014, background): “oothly deﬁned on C C if C is a convex normal neighborhood where we also have s(x;y) = s(y;x). The class of the convex normal neighborhoods of a point p 2Mis a fundamental system of neighborhoods of p [22, 3]. In Euclidean manifolds s deﬁned as above is everywhere nonnegative with the standard Euclid”