I am trying to follow a derivation in this paper from Wald

Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation

$$ Q/m \leq 2 B_0 m$$

where $Q$ is the system charge, $m$ the mass and $B_0$ the magnetic field. This equation in in geometrized units such that $c=G=1$ (as defined at the start of the paper).

Now, it is given as an example that if $B_0 \sim 10^{-4} $ gauss and $m = M_{\odot} \sim 2 \times 10^{30}$ kg, then $Q/m \sim 10^{-24}$, but I am struggling to show this

Specifically, I feel like if I convert both $B$ and $m$ from $[SI]\rightarrow [Geo]$ and then plug the values in to the top equation, then I should get the answer $10^{-24}$.

I am following the conversion as outlined in Section 4 of these notes such that,

$$B [SI] = G^{-1} c^{-4} \times B[Geo]$$ $$m [SI] = G^{-1} c^{2} \times m[Geo]$$

but this does not seem to produce the correct answer. Any guidance?

  • $\begingroup$ I cannot access this paper, but the inequality that you quote seems to be wrong on dimensional ground.The lhs is charge (length in geom. units) divided by mass (again length in geom. units), so it is a pure number , as you state.But the rhs is a magnetic field (length in geom. units) times mass (again length in geom.units) , so rhs has dimension of length squared.So please recheck this inequality.Also note that Wald is using gaussian units , not SI for the magnetic field. Also your conversion formula for B is wrong,I suggest you quote (copy) part of the paper , so we can check the calculation $\endgroup$ – magma Aug 29 '18 at 14:28
  • $\begingroup$ @magma I have the same problem: there is something off with the units. Here: booksc.xyz/book/11573639/fa68e3 you can find the paper. $\endgroup$ – mattiav27 Aug 27 at 7:59
  • $\begingroup$ @magma I am trying to convert the formula Q=2BJ to cgs, where Q is the charge B is the magnetic field and J the angular momentum. It seems like that there is a factor 1/s too much. $\endgroup$ – mattiav27 Aug 27 at 8:02

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