# Are extra dimensions timelike or spacelike?

In special relativity there is a clear difference between spatial and temporal dimensions of spacetime due to the Minkowski metric diag(-1,1,1,1). In higher dimensional theories (10- and 26-dimensional string theories) does this asymmetry continue with additional dimensions being specifically time- or space-like or is there no clear difference?

We want to study the classical and quantum dynamics of a one-dimensional object, a string. The string moves in $$D$$ flat spacetime dimensions, with metric $$\eta_{\mu \nu} = \mathrm{diag}(-,+,+,\cdots,+)$$.