Abstract
Abstract
A natural codimension one isometric embedding of each
(
n
+
1
)
-dimensional spherical Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime
I
×
f
S
n
in the
(
n
+
2
)
-dimensional Lorentz–Minkowski spacetime
L
n
+
2
permits to contemplate
I
×
f
S
n
as a rotation Lorentzian hypersurface in
L
n
+
2
. After a detailed study of such Lorentzian hypersurfaces, any k-dimensional spacelike submanifold of such an FLRW spacetime can be contemplated as a spacelike submanifold of
L
n
+
2
. Then, we use that situation to study k-dimensional stationary (i.e. of zero mean curvature vector field) spacelike submanifolds of the FLRW spacetime. In particular, we prove a wide extension of the Lorentzian version of the classical Takahashi theorem, giving a characterization of stationary spacelike submanifolds of
I
×
f
S
n
when contemplating them as spacelike submanifolds of
L
n
+
2
.
Subject
General Physics and Astronomy,Mathematical Physics,Modeling and Simulation,Statistics and Probability,Statistical and Nonlinear Physics