# Dimensional analysis for gravitational radiation expression

on this paper, please refer to equation 2.117 for the power emitted for a rotating mass system:

$$P = - \frac{128}{5} G M^2 R^4 \Omega^6$$

power in cgs should be (g is grams, m is meter, s is seconds):

$$g m^2 s^{-3}$$

now, $G$ is in $m^3 g^{-1} s^{-2}$ and $\Omega$ is in $s^{-1}$ so 2.117 right hand side is

$$m^7 g s^{-8}$$

so, i'm going to infer that the right hand side is missing a factor of $\frac{1}{c^5}$, so the dimensionally accurate expression for power (without weird normalized units) is;

$$P = - \frac{128}{5 c^5} G M^2 R^4 \Omega^6$$

is that dimensional analysis accurate?

One thing that you may have overlooked are dimensions hidden in the 128/5 constant. It would take a while for me to work through the paper to see where that comes from, but it would be easy to overlook those.
• The linked paper mentions they use units in which $c=1$ twice (in the appendix), so the concern is unnecessary. Aug 8, 2014 at 4:02