# fields at infinity

06 May 2020The Poisson-equation in electrostatics, \(\Delta\Phi = -4\pi\rho\) is solved by the electric potential \(\Phi = 4\pi Q/r\) for a point charge and vanishes at infinity, whereas the Poisson equation in gravity, \(\Delta\Phi = 4\pi G\rho\) is solved by \(\Phi = -GM/r\) for a point mass, but you can add \(\lambda r^2\) to the solution, which diverges as \(r\rightarrow\infty\): Is it possible to reconcile both cases? Are there issues with the Green-theorems, which require vanishing fields for uniqueness of solutions?