general relativity - What is the relationship between $a$ and $m$

$a$ is defined in HERE

What is the relationship between the length-scale $a$ and the mass $m$?

Answer

According to Schutz (chapter 11) for the Schwarzschild metric $dr/d\phi$ is given by:

$$\left(\frac{dr}{d\phi}\right)^2 = \frac{E^2}{L^2}r^4 - \left(1 - \frac{r_s}{r}\right)\left(\frac{r^4}{L^2} + r^2\right)$$

where:

$$\begin{align} E &= \frac{p_0}{m} \\ L &= \frac{p_\phi}{m} \end{align}$$

Comparing this with the equation in the Wikipedia article we find:

$$a = L = \frac{p_\phi}{m} = r^2\frac{p^\phi}{m}$$

Though this makes $a$ an angular velocity rather than a length scale.