 
Summary: ASYMPTOTIC BEHAVIOR OF STATIC AND STATIONARY
VACUUM SPACETIMES
Michael T. ANDERSON
Dept. of Mathematics, S.U.N.Y. at Stony Brook, Stony Brook, NY 11794, USA
Email: anderson@math.sunysb.edu
Let (M; g) be an Einstein vacuum chronological spacetime. The spacetime is
stationary if it admits a timelike Killing eld X = @=@t, and static if the Killing eld
is hypersurface orthogonal. Let u =
p
g(X; X) > 0 and let : (M; g) ! (S; g S )
be the projection to the orbit space of the R action generated by X . We recall the
following classical and wellknown results of Lichnerowicz [1,x85, x90], c.f. however
[2] for an earlier version.
Lichnerowicz Theorems. (I). Suppose (M; g) is a geodesically complete
static vacuum spacetime, with u(x) ! 1, as x !1 in S. Then (M; g) is
at.
(II). Suppose (M; g) is a geodesically complete stationary vacuum spacetime
which is asymptotically
at, (AF). Then (M; g) is
at.
Physically, these results appear quite satisfying. If the spacetime is vacuum
and geodesically complete, then there are no "matter or energy sources" contained
in the spacetime. Under the asymptotic conditions at innity, one then concludes
