Planck mass from compactification volume
= Planck mass from compactification volume
{c}
{title2=$M_{\rm Pl}^2=M_*^{n+2}V_n$}
For an unwarped product metric with fixed compact volume $V_n$, integrating the higher-dimensional <Einstein-Hilbert action> gives $M_{\rm Pl}^2=M_*^{n+2}V_n$ when the action coefficient is $M_D^{D-2}/2$. The <reduced Planck mass> convention must be distinguished from the unreduced one, and stabilizing the internal metric is a separate dynamical issue.