منابع مشابه
Rigid Singularity Theorem in Globally Hyperbolic Spacetimes
30 years ago, Penrose-Hawking have shown that spacetimes are geodesically incomplete under some physically reasonable conditions [1] [2] [3] [4]. The generic condition is the key assumption to induce singularities rigidly. Geroch improved these theorems with “no observer horizon” condition in place of the generic condition for the spatially closed universe [5,6]. Here, the “no observer horizon”...
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We study the flat (n+1)-spacetimes Y admitting a Cauchy surface diffeomorphic to a compact hyperbolic n-manifold M . Roughly speaking, we show how to construct a canonical future complete one, Yρ, among all such spacetimes sharing a same holonomy ρ. We study the geometry of Yρ in terms of its canonical cosmological time (CT). In particular we study the asymptotic behaviour of the level surfaces...
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Connes’ functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d’Alembert operator and the causal functions of a globally hyperbolic spacetime. As a step of the presented machinery, a proof of the almosteverywhere smoothness of the Lorentzian distance considered as a function of one of the two arguments is given. Afterwar...
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This is the last article in a series of three initiated by the second author. We elaborate on the concepts and theorems constructed in the previous articles. In particular, we prove that the GH and the GGH uniformities previously introduced on the moduli space of isometry classes of globally hyperbolic spacetimes are different, but the Cauchy sequences which give rise to well-defined limit spac...
متن کاملQuantum Energy Inequalities and Local Covariance I: Globally Hyperbolic Spacetimes
We begin a systematic study of Quantum Energy Inequalities (QEIs) in relation to local covari-ance. We define notions of locally covariant QEIs of both 'absolute' and 'difference' types and show that existing QEIs satisfy these conditions. Local covariance permits us to place constraints on the renormalised stress-energy tensor in one spacetime using QEIs derived in another, in subregions where...
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2005
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2004.05.002