Axisymmetric logarithmic gravitational potential
= Axisymmetric logarithmic gravitational potential
{title2=$\Phi=\tfrac12V^2\log(R^2+z^2/q^2)$}
An axisymmetric logarithmic <Newtonian gravitational potential> has spheroidal equipotential surfaces and a <flat galaxy rotation curve>: $R\Phi_R(R,0)=V^2$. The singular model is defined away from the origin; a fixed reference length makes the logarithm dimensionless. Its central $r^{-2}$ <mass density> cusp is locally integrable, but its total <mass> diverges at large radius.