- #1
Mentz114
- 5,432
- 292
Reading this paper
http://lanl.arxiv.org/abs/gr-qc/9611042v1
I'm baffled by this bit on page 3,
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 toldThe metric of a stationary space-time with time-like Killing vector K = ∂/∂t has the form
ds2 = r(dt + ωidxi)2 − r−1dℓ2 (i, j, ... = 1, 2, 3), (2.1)
where r = K·K is the length square of the Killing vector, ωidxi a 1-form, and dℓ2 = gijdxidxj 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.