Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems General Relativity: An Introduction for Physicists · Problem 17.4
Linearised general relativity — Hobson, Efstathiou & Lasenby
Physics · trace-reverse-linearised-einstein-equations
Problem The trace reverse of h μ ν h_{\mu\nu} h μν h ˉ μ ν ≡ h μ ν − 1 2 η μ ν h . \bar{h}_{\mu\nu} \equiv h_{\mu\nu} - \tfrac{1}{2}\eta_{\mu\nu}h. h ˉ μν ≡ h μν − 2 1 η μν h . h ˉ = − h \bar{h} = -h h ˉ = − h h ˉ ˉ μ ν = h μ ν \bar{\bar{h}}_{\mu\nu} = h_{\mu\nu} h ˉ ˉ μν = h μν □ 2 h ˉ μ ν + η μ ν ∂ ρ ∂ σ h ˉ ρ σ − ∂ ν ∂ ρ h ˉ μ ρ − ∂ μ ∂ ρ h ˉ ν ρ = − 2 κ T μ ν . \Box^2\bar{h}_{\mu\nu} + \eta_{\mu\nu}\partial_{\rho}\partial_{\sigma}\bar{h}^{\rho\sigma} - \partial_{\nu}\partial_{\rho}\bar{h}^{\rho}_{\mu} - \partial_{\mu}\partial_{\rho}\bar{h}^{\rho}_{\nu} = -2\kappa T_{\mu\nu}. □ 2 h ˉ μν + η μν ∂ ρ ∂ σ h ˉ ρ σ − ∂ ν ∂ ρ h ˉ μ ρ − ∂ μ ∂ ρ h ˉ ν ρ = − 2 κ T μν . Browse the problem library