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Gravitational Screening

Calculations of the stopping power of a medium lead to divergent integrals in gravitational theory as they do in the analogous electromagnetic problem. In the em case, one introduces (normally in an arbitrary manner) the Debye length as a cutoff at large distances to remove the divergence. We show here that in the Newtonian gravitational analogue the distant cutoff problem is solved by including the self-gravity of the medium. Then the Jeans length appears naturally as a cutoff. Despite the different sign of the coupling constant from the case of the electric plasma, the same sort of theory works in both cases and removes the need of introducing ad hoc cutoffs from both of them.