multipole expansion

21 May 2025

Can you construct a multipole expansion for the Poisson-equation \(\Delta\Phi = 4\pi (G) \rho\) in every number of dimensions, in particular in \(2d\)?

bonus question: Is the multipole expansion (in \(3d\)) possible if you include a classical cosmological constant $\lambda$, in the form \(\Delta\Phi = 4\pi (G) \rho + \lambda\)?

second bonus question: Does the multipole expansion depend on a Yukawa-term \((\Delta - m^2)\Phi = 4\pi (G) \rho\)?