Summary
We discuss the interaction between the matter content of a closed physical space, associated with a generic gravitational configuration (i.e. without symmetries), and the topology of the underlying closed three-manifoldS. We show that, within the context of the conformal approach to the initial-value problem, the presence of enough matter and radiation favours those topologies we expect, on heuristic grounds, to be actually encountered, namely the three-sphere topology, or the (S 1×S 2)-worm-hole topology. We also argue that such topologies leave, as far as the field equations are concerned, more room to possible gravitational initial data sets.
Riassunto
Si discute l’interazione fra il contenuto energetico di uno spazio fisico chiuso, descrivente una configurazione gravitazionale generica (cioè senza simmetrie), e la struttura topologica della corrispondente varietà tridimensionale chiusaS. Si dimostra, nel contesto della trattazione conforme del problema ai valori iniziali, che la presenza di materia e radiazione in quantità sufficienti favorisce quelle topologie che, su basi euristiche, ci si aspetta d’incontrare, vale a dire la topologia della tre-sfera e la topologia di un «worm-hole» di tipoS 1×S 2. Si osserva anche che, per quanto riguarda le equazioni di campo, tali topologie lasciano piú spazio a possibili insiemi di dati iniziali.
Резюме
Мы обсуждаем взаимодействия между энергетическим содержанием замкнутого физического пространства, связанного с характерной гравитационной конфигурацией (т.е. без симметрий) и топологией соответствующего замкнутого трехмерного множестваS. Мы показываем, что в контексте конформного подхода к проблеме начальных значений наличие значительного количества вещества и излучения отдает предпочтение тем топологиям, которые, как мы ожидаем на эвристической основе, действительно встречаются, а именно, топология трехмерной сферы или топологияS 1×S 2. Мы также доказываем, что такие топологии оставляют больше пространства для возможных систем гравитационных начальных данных.
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Carfora, M. Initial data sets and the topology of closed three-manifolds in general relativity. Nuovo Cim B 77, 143–161 (1983). https://doi.org/10.1007/BF02721481
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DOI: https://doi.org/10.1007/BF02721481