Trace-reversed Einstein field equations in D dimensions

For

D > 2

, tracing and substituting back gives

R_{μν} = κ (T_{μν} - \frac{1}{D - 2} g_{μν} T) .

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- Ricci curvature sourced by a Klein-Gordon scalar field Trace-reversed Einstein field equations in D dimensions

Ricci curvature sourced by a Klein-Gordon scalar field

For the conserved scalar stress tensor above,

R_{μν} = \frac{κ}{2} [\nabla_{μ} ϕ \nabla_{ν} ϕ + \frac{m ^{2}}{D - 2} g_{μν} ϕ^{2}] .

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Past exam of the mathematics course of the University of Cambridge / 2020 / ii / Paper 4 / 37D / i / Solution
Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 38D / b / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 1 / 38B / b / Solution

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