F eb 1 99 7 Global Foliations of Vacuum Spacetimes with T 2 Isometry
نویسنده
چکیده
We prove a global existence theorem (with respect to a geometricallydefined time) for globally hyperbolic solutions of the vacuum Einstein equations which admit a T 2 isometry group with two-dimensional spacelike orbits, acting on T 3 spacelike surfaces. Visiting Scientist: Max-Planck-Institut für Gravitationsphysik (Albert-EinsteinInstitut) Schlaatzweg 1, 14473 Potsdam, Germany
منابع مشابه
ar X iv : g r - qc / 0 21 10 63 v 1 1 8 N ov 2 00 2 Existence of CMC and constant areal time foliations in T 2 symmetric spacetimes with Vlasov matter
The global structure of solutions of the Einstein equations coupled to the Vlasov equation is investigated in the presence of a twodimensional symmetry group. It is shown that there exist global CMC and areal time foliations. The proof is based on long-time existence theorems for the partial differential equations resulting from the EinsteinVlasov system when conformal or areal coordinates are ...
متن کاملVacuum Branes in D - Dimensional Static Spacetimes with Spatial Symmetry IO ( D − 2 ) , O ( D − 1 ) or O + ( D −
In this paper, we give a complete classification of vacuum branes, i.e., everywhere umbilical time-like hypersurfaces whose extrinsic curvature is a constant multiple of the induced metric, Kμν = σgμν , in D-dimensional static spacetimes with spatial symmetry G(D−2, K), where G(n,K) is the isometry group of an n-dimensional space with constant sectional curvature K. D ≥ 4 is assumed. It is show...
متن کاملNo-horizon theorem for spacetimes with spacelike G1 isometry groups
We consider four-dimensional spacetimes (M,g) which obey the Einstein equations G = T, and admit a global spacelike G1 = R isometry group. By means of dimensional reduction and local analyis on the reduced (2 + 1) spacetime, we obtain a sufficient condition on T which guarantees that (M,g) cannot contain apparent horizons. Given any (3 + 1) spacetime with spacelike translational isometry, the n...
متن کاملGlobal Prescribed Mean Curvature foliations in cosmological spacetimes with matter Part II
This second part is devoted to the investigation of global properties of Prescribed Mean Curvature (PMC) foliations in cosmological spacetimes with local U(1)× U(1) symmetry and matter described by the Vlasov equation. It turns out, that these spacetimes admit a global foliation by PMC surfaces, as well, but the techniques to achieve this goal are more complex than in the cases considered in pa...
متن کامل1 Vacuum branes in D-dimensional static spacetimes with spatial symmetry IO(D − 2), O(D − 1) or O+(D − 2, 1)
In this paper, we give a complete classification of everywhere umbilical time-like hypersurfaces, called vacuum branes, whose extrinsic curvature is a constant multiple of the induced metric, Kμν = σgμν , in D-dimensional static spacetimes with spatial symmetry G(D − 2,K), where G(n,K) is the isometry group of a n-dimensional space with constant sectional curvature K. D ≥ 4 is assumed. It is sh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997