# local field equations and nonlocal components

08 Jun 2016The Poisson-equation of electrostatics (or Newtonian gravity) links the second derivatives of the potential \(\Phi\) to the local charge (or matter) density \(\rho\), by requiring \(\Delta\Phi=4\pi(G)\rho\). This is nice, because \(\Delta\Phi\) is the trace of the Hessian \(\partial_i\partial_j\Phi\), making it invariant under rotations and therefore generates a spherically symmetric potential. but what fixes the off-diagonal components? Would there be a possibility to measure them directly?