Kaluza-Klein with constant scalar field


coordinate convention: $dx^0 = c dt, \partial_0 = \frac{1}{c} \partial_t$

$c = $ $\cdot \frac{m}{s} = 1 = $ the speed of light.
$G = $ $\cdot \frac{m^3}{kg \cdot s^2} = 1 = $ gravitational constant.
$k_e = $ $\cdot \frac{kg \cdot m^3}{C^2 \cdot s^2}$ = Coulomb's constant (typically $\frac{1}{4 \pi \epsilon_0}$).
$\sqrt{{\frac{1}{G}} {{k_e}}}$ = {=={ sqrt_Coulomb_constant_over_gravitational_constant_in_kg_per_C = Math.sqrt(Coulomb_constant_in_kg_m3_per_C2_s2 / gravitational_constant_in_m3_per_kg_s2) }==} $ \cdot \frac{kg}{C} = 1 =$ conversion from kg to C
$kg = $ {=={ 1 / sqrt_Coulomb_constant_over_gravitational_constant_in_kg_per_C }==} $C$.