WebJan 27, 2024 · Moreover, since a globally hyperbolic spacetime is causally simple (see, e.g., [ 4, Proposition 3.16]), if ( M, g) is globally hyperbolic then J± ( x0, t0) are closed and \big (x_ {1}, {\Delta }^ {\pm } (x_ {0},x_ {1})\big )\in J^ {\pm } (x_ {0},t_ {0}). The following proposition holds. Proposition 5 WebOct 18, 2024 · The Cauchy slicings for globally hyperbolic spacetimes and their relation with the causal boundary are surveyed and revisited, starting at the seminal conformal …
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Weba spacetime outside its globally hyperbolic region (the boundary of the globally hyperbolic region is called the Cauchy horizon). The claim of scc is that, for most spacetimes, such extensions cannot be made. Note that in most cases one may use the constraints (3) to solve for A and d,A, given U and d ... WebDec 20, 2024 · the spacetime is globally hyperbolic with a non-compact Cauchy surface \Sigma , (3) there exists a closed trapped surface \mathscr {T}. The proof of this theorem is derived by contradiction (see, e.g., [ 47, 48 ]). It starts by assuming that the spacetime is null geodesically complete. chat puree
[1401.2026] Quantum fields in curved spacetime - arXiv.org
WebThere exists a global time function on . This is a scalar field on whose gradient is everywhere timelike and future-directed. This global time function gives us a stable way to distinguish between future and past for each point of the spacetime (and so we have no causal violations). Globally hyperbolic [ edit] is strongly causal and every set WebFor instance, the phase space of a free KG field in a globally hyperbolic spacetime can be described (in the canonical approach) by the symplectic vector space (Γ, Ω), where Γ is the (infinite-dimensional) linear space coordinatized by the configurations and momenta of the field, {(φ (y), π (y))} where y ∈ Σ, and Ω is the canonical ... Weba spacetime can be reconstructed (in a purely order-theoretical manner) from a dense discrete set. In particular, this suggests that a globally hyperbolic spacetime is linked … chat pusdienas