= Timelike cone
{title2=$\{v:g(v,v)>0\}\quad\text{for signature }(+---)$}
The <timelike cone> is the open set of nonzero <tangent vectors> with timelike squared norm. It has future and past components once a time <orientation> is chosen. Homogeneity extends an identity for unit <timelike vectors> to this whole open set. In particular, if a symmetric <quadratic form> vanishes on every <timelike vector>, its polynomial vanishes on an open set and therefore vanishes identically. This observation proves the converse from <geodesic> first integrals to the Killing equation.
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