Is there a 1D Lorentzian manifold?

Question

In Nakahara (Theorem 7.4, Pg 291) we have for an $r$-form on an $m$-dimensional manifold $$ * *\omega = (-1)^{r(m-r)}\omega$$ when Riemannian and $$ * *\omega = (-1)^{1+r(m-r)}\omega$$ when Lorentzian. So, for $m = 1$, it is possible to have $$ * * = -1$$ for a $0$-form in $1D$ Lorentizan manifold. Hence, my question. Does $1D$ Lorentizian manifold makes sense?