General Relativity: An Introduction for Physicists · Problem 7.1

The equivalence principle and spacetime curvature — Hobson, Efstathiou & Lasenby

Physics · newtonian-gravitational-potential

Problem

From Poisson's equation ∇2Φ=4πGρ\nabla^2\Phi = 4\pi G\rho show that the gravitational potential outside a spherical object of mass MM at a radial distance rr from its centre is given by Φ(r)=−GM/r\Phi(r) = -GM/r. What is the form of Φ(r)\Phi(r) inside a uniform spherical body?

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