  Some time ago Dvali, Gabadadze and Senjanovic (hep-ph/9910207) discussed
brane world scenarios with time-like extra dimensions. In this paper we
construct a solitonic 3-brane solution in the 5-dimensional
Einstein-Hilbert-Gauss-Bonnet theory with the space-time signature (-,+,+,+,-).
The direction transverse to the brane is the second time-like direction. The
solitonic brane is $\delta$-function like, and has the property that gravity is
completely localized on the brane. That is, there are no propagating degrees of
freedom in the bulk, while on the brane we have purely 4-dimensional Einstein
gravity. In particular, there are no propagating tachyonic or negative norm
states even though the extra dimension is time-like.
