Time-like extra dimensions without tachyons or ghosts

Some time ago Dvali, Gabadadze and Senjanović hep-ph/9910207 discussed brane world scenarios with time-like extra dimensions. In this Letter 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 δ-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.