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http://lanl.arxiv.org/abs/gr-qc/9611042v1

I'm baffled by this bit on page 3,

In a footnote on page 4 we are told The metric of a stationary space-time with time-like Killing vector K = ∂/∂t has the form

ds^{2}= r(dt + ω_{i}dx^{i})^{2}− r^{−1}dℓ^{2}(i, j, ... = 1, 2, 3), (2.1)

where r = K·K is the length square of the Killing vector, ω_{i}dx^{i}a 1-form, and dℓ^{2}= g_{ij}dx^{i}dx^{j}the metric in the 3-space S of Killing trajectories.

By this, K·K = 0 and equation 2.1 is nonsense. What have I missed ? Vectors in the tangent 3-space are set in boldface. A dot notation (.) is used for a scalar product with respect to the 3-metric.

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# Problem with notation ?

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