 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-4/37e/a/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

In the static limit, the supplied linearized Riemann tensor gives

R_{00} = δ^{ij} R_{i 0 j 0} = - \frac{1}{2} \nabla^{2} h_{00} .

R = - κ T

. Here

T ≃ - ρ

, so

R = κ ρ

. The

00

R_{00} - \frac{1}{2} η_{00} R = R_{00} + \frac{1}{2} R = κ ρ,

which yields

R_{00} = κ ρ /2

. Combining the two expressions for

R_{00}

gives

- \nabla^{2} h_{00} = κ ρ .

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