Units of the metric tensor or how to get the unit right for the line element

In this answer it is stated that the metric tensor elements have no physical unit, i.e. $[g_{\mu\nu}] = 1$. What is the convention to get the physical unit of the line element $ds = g_{\mu\nu}dx^\mu dx^\nu$ right. I assume that $[dx^0] = s$ (seconds), and $[dx^i] = m$ (meter) for $i=1,2,3$. The flat spacetime, $$ds^2 = -c^2dt^2 + dx^2+dy^2+dz^2$$

would suggest that $[g_{00}] = [c^2] = (m/s)^2$.

What is a (the) convention to get the units right.

• There is no universal convention on this. As an example of how conventions can vary, see Dicke, Phys Rev 125 (1962) 2163. He lets the metric have units of distance. I have a detailed discussion in section 5.11 of my GR book, lightandmatter.com/genrel . – Ben Crowell Feb 25 '18 at 16:23
• @BenCrowell - have you considered publishing your book as a paperback using Kindle Direct Publishing? It's free and reasonably straightforward. You just need a content file pdf and a cover pdf. Apologies if this sort of comment should be in chat. – Peter4075 Apr 3 at 16:49

The typical convention is $x_0=ct$, so $[dx_0]=[dx_i]=~\rm m$.
Although people frequently set $c=1$ to simplify things, and then the whole point is moot.