One way to fix this factor is indeed to fix the parametrization. But the point is that it is not the only way.A. Neumaier said:But (for a curve) this tangent vector is unique only up to a (positive or negative) factor.
So how do you fix it without getting a spurious sign in your ds?Demystifier said:One way to fix this factor is indeed to fix the parametrization. But the point is that it is not the only way.
If the curve is oriented (which is a much weaker requirement than that it is parameterized), then the sign is chosen such that ##s## increases in the direction of orientation. In my case, the orientation at each point is defined by the direction of the vector ##V^{\mu}##, to which the curve is tangent. Note also that in my paper ##\Omega## in Eq. (111) is positive.A. Neumaier said:So how do you fix it without getting a spurious sign in your ds?