General Relativity: An Introduction for Physicists · Problem 17.5

Linearised general relativity — Hobson, Efstathiou & Lasenby

Physics · covariant-riemann-tensor-gauge-invariance

Problem

Obtain an expression for the covariant components RσμνρR_{\sigma\mu\nu\rho} of the linearised Riemann tensor in Exercise 17.3 and show that it is invariant under a gauge transformation of the form (17.5). Hence show that the linearised Einstein field equations are also invariant under such a gauge transformation.

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