= Lorentzian metric
{c}
{title2=$\operatorname{signature}(g)=(-,+,\ldots,+)$}
A Lorentzian metric is a smooth nondegenerate symmetric <metric tensor> with one negative and all other positive directions, or its opposite-sign convention. At each point, a nonzero tangent is timelike, null or spacelike according as $g(v,v)$ is negative, zero or positive in the first convention. Unlike a <Riemannian metric>, it gives a light cone rather than a positive norm. <Minkowski spacetime> is its constant flat model, and <proper time> along a timelike curve is $\int\sqrt{-g(\dot\gamma,\dot\gamma)}\,du$.
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