caa a22 4500 606210083 CHVBK 20210128101031.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00032-015-0241-2 doi (NATIONALLICENCE)springer-10.1007/s00032-015-0241-2 Myers and Hawking Theorems: Geometry for the Limits of the Universe [Elektronische Daten] [Pablo Morales Álvarez, Miguel Sánchez] It is known that the celebrated theorem by Hawking which assures the existence of a Big-Bang under physically motivated hypotheses, uses geometric ideas inspired in classical Myers theorem. Our aim here is to go a step further: first, a result which can be interpreted as the exact analogy in pure Riemannian geometry to Hawking theorem will be proven and, then, the isomorphic role of the hypotheses in both theorems will be analyzed. This will provide some interesting links between Riemannian and Lorentzian geometries, as well as an introduction to the latter. The reader interested only in Riemannian Geometry can regard this new result as a simple application of Myers theorem combined with the properties of focal points. However, readers with broader perspectives will learn that when a geometer thinks in our space as a complete Riemannian manifold, a relativist may think in our spacetime as predictable, or that suitable bounds on the Ricci tensor will force geodesics either to converge in the space or to join in the time. Moreover, the limitation of the distance from any point to a hypersurface in a Riemannian manifold, may turn out into a catastrophic relativistic limit for the duration of our physical Universe. Springer Basel, 2015 Focal points nationallicence expanding hypersurface nationallicence positive Ricci curvature nationallicence singularity theorems nationallicence separating and Cauchy hypersurfaces nationallicence timelike convergence nationallicence Morales Álvarez Pablo Departamento de Geometría y Topología, Universidad de Granada, Facultad de Ciencias, Campus Fuentenueva s/n, E-18071, Granada, Spain aut Sánchez Miguel Departamento de Geometría y Topología, Universidad de Granada, Facultad de Ciencias, Campus Fuentenueva s/n, E-18071, Granada, Spain aut Milan Journal of Mathematics Springer Basel 83/2(2015-12-01), 295-311 1424-9286 83:2<295 2015 83 32 https://doi.org/10.1007/s00032-015-0241-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00032-015-0241-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Morales Álvarez Pablo Departamento de Geometría y Topología, Universidad de Granada, Facultad de Ciencias, Campus Fuentenueva s/n, E-18071, Granada, Spain aut NATIONALLICENCE 700 1- Sánchez Miguel Departamento de Geometría y Topología, Universidad de Granada, Facultad de Ciencias, Campus Fuentenueva s/n, E-18071, Granada, Spain aut NATIONALLICENCE 773 0- Milan Journal of Mathematics Springer Basel 83/2(2015-12-01), 295-311 1424-9286 83:2<295 2015 83 32