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Titlebook: Recent Trends in Lorentzian Geometry; Miguel Sánchez,MIguel Ortega,Alfonso Romero Conference proceedings 2013 Springer Science+Business Me

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The Geometry of Collapsing Isotropic Fluids,of the most intriguing problems in gravitational collapse is that perfect fluids are a direct, physically interesting generalization of the so-called Tolman–Bondi–Lemaitre (TBL) solution, which is one of the few known-in-details solutions dynamically collapsing to a singularity. The TBL solution is
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Can We Make a Finsler Metric Complete by a Trivial Projective Change?,rd and backward complete by a trivial projective change.Though the problem is purely Finslerian, it was inspired by Lorentz geometry and mathematical relativity: it was observed that it is possible to understand the light-like geodesics of a (normalized, standard) stationary 4-dimensional space time
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The C-Boundary Construction of SpaceTimes: Application to Stationary Kerr SpaceTime,, completing some points which were suggested in the original works. Second, we are going to apply these results to provide a precise description of the c-boundary of the stationary part of (slow rotating) Kerr space time.
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On the Isometry Group of Lorentz Manifolds, is cast in the language of .-structures. In the second part of this chapter, we will review some recent results on the classification of groups acting isometrically on compact Lorentz manifolds and on the geometry of compact manifolds whose isometry group is non compact.
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Hyperbolic Metrics on Riemann Surfaces and Space-Like CMC-1 Surfaces in de Sitter 3-Space,there is a bijection between the moduli space of ...-catenoids and the moduli space of co-orientable extended hyperbolic metrics with two regular singularities, a classification of such hyperbolic metrics is also given. (Co-orientability of extended hyperbolic metrics is defined in this paper.)
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,Calabi–Bernstein Results and Parabolicity of Maximal Surfaces in Lorentzian Product Spaces,extensions and generalizations of it made by several authors in recent years, and describing also some recent results obtained by the authors for maximal surfaces immersed in Lorentzian product spaces.
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Stability of Marginally Outer Trapped Surfaces and Applications,nd present some of its consequences. In particular I will summarize the implications of stability on the topology of MOTS, their role as barriers, the interplay between stability and space–times symmetries and the stability of Killing horizons.
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