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In Minkowski spacetime with metric signature $(-,+,+,+)$, write two nonzero future-pointing null vectors as $A=a(1,\mathbf{n})$ and $B=b(1,\mathbf{m})$, where $a,b>0$ and $\mathbf{n},\mathbf{m}$ are unit vectors. Their Lorentzian inner product givesThus their sum is a future-pointing causal vector. It is a null vector exactly when the spatial directions coincide, and a timelike vector otherwise. The positivity of the time components is essential: adding past- and future-pointing null vectors can instead produce a spacelike vector.

A timelike vector $v$ obeys $g(v,v)<0$ in metric signature $(-,+,+,+)$. Its orthogonal complement has positive-definite metric; the two timelike cones give the local future and past choices.

A time orientation is a continuous choice of future cone throughout a time-orientable spacetime. A continuous nonzero timelike vector field supplies such a choice. For metric signature $(-,+,+,+)$, a nonzero causal vector $Z$ is future-directed relative to a future timelike $W$ exactly when $g(W,Z)<0$.