### 8.1 Geometric interpretation of v_{a}

Assuming that the derivatives of and with respect to time and space tend to zero, the
expansions (37) – (38) imply (recall that )
where the kinetic energy density is given by Equation (28). In other words, from a geometric point of
view, is the same object as in the polarized case. Furthermore, it is possible to prove that if expansions
of the form of Equations (37) – (38) hold with , then the Kretschmann scalar is unbounded
along causal curves whose -component converges to in the direction towards the singularity; see
Section 7.4. As in the polarized case, we shall refer to as the velocity. The condition
will in the future be referred to as low velocity, whereas will be referred to as high
velocity.