Solving Poisson's equation gives the gravitational potential Φ Φ ( r ) = − − 4 π π G ρ ρ 0 R s 3 r ln ⁡ ⁡ ( 1 + r R s ) with the limits lim r → → ∞ ∞ Φ Φ = 0 and lim r → → 0 Φ Φ = − − 4 π π G ρ ρ 0 R s 2 .