Sectional curvature of standard static space-times

Abstract

Egrilmis carpm manifoldlarnn egrilik ile ilgili geometrik ozellikleri verildi.Lorentz egrilmis carpmlarnn nedensel yaps incelendi. Ozellikle, egrilmis carpm uzay-zaman modellerinden en iyi bilinen iki ornegi, yani, genellestirilmisRobertson-Walker uzay-zamanlar ve tek bicimli statik uzay-zamanlar calsld.Tek bicimli statik uzay-zamanlarn kesitsel egrilikleri belirlendi ve negatif olmayankesitsel egrilige sahip olabilmeleri icin gerekli kosullar elde edildi. Bunlarn sonucuolarak, tekillik teoremleri tek bicimli statik uzay-zamanlara uygulanabilir.Anahtar sozcukler: yar-Riemann geometri, egrilmis carpmlar, GenellestirilmisRobertson-Walker uzay-zamanlar, Tek bicimli statik uzay-zamanlar, kesitselegrilik, jeodesik.

Curvature related geometric properties of warped product manifolds are given.The casual structure of Lorentzian warped products is reviewed. In particular,two well-known examples of warped product space-times models, i.e, generalizedRobertson-Walker and standard static space-times are studied. The sectionalcurvature of a standard static space-time is established and some conditions areobtained to have nonnegative sectional curvature so that applications of singularity theorems to a standard static space-time can be considered.Keywords: semi-Riemannian geometry, warped products, Generalized RobertsonWalker space-times, Standard Static space-times, sectional curvature, geodesic