Existence of Constant Mean Curvature Hypersurfaces in Asymptotically Flat Spacetimes

Constant mean curvature foliations in cosmological spacetimes

Foliations by constant mean curvature hypersurfaces provide a possibility of defining a preferred time coordinate in general relativity. In the following various conjectures are made about the existence of foliations of this kind in spacetimes satisfying the strong energy condition and possessing compact Cauchy hypersurfaces. Recent progress on proving these conjectures under supplementary assu...

Van Stockum–Bonnor Spacetimes of Rigidly Rotating Dust

We discuss different classes of van Stockum spacetimes which are stationary and axisymmetric spacetimes of dust rotating rigidly on trajectories of the time translation Killing vector. The flow has no Newtonian limit. Asymptotically flat solutions are not physically viable. As an example we construct a sequence of asymptotically flat internal multipolar solutions. The corresponding sequence of ...

Existence of constant mean curvature foliations in spacetimes with two-dimensional local symmetry

It is shown that in a class of maximal globally hyperbolic spacetimes admitting two local Killing vectors, the past (defined with respect to an appropriate time orientation) of any compact constant mean curvature hypersurface can be covered by a foliation of compact constant mean curvature hypersurfaces. Moreover, the mean curvature of the leaves of this foliation takes on arbitrarily negative ...

Hypersurfaces with Constant Mean Curvature in a Lorentzian Space Form

Spacetimes admitting quasi-conformal curvature tensor

‎The object of the present paper is to study spacetimes admitting‎ ‎quasi-conformal curvature tensor‎. ‎At first we prove that a quasi-conformally flat spacetime is Einstein‎ ‎and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying‎ ‎Einstein's field equation with cosmological constant is covariant constant‎. ‎Next‎, ‎we prove that if the perfect flui...