Conceptual Pitfalls in Teaching the Linearized Approximation in Introductory General Relativity

Abstract

The decomposition of the metric tensor into a flat background plus small perturbations used in linearized general relativity is often a source of confusion for the student because these two parts are only Lorentz-invariant but not generally covariant. The underlying, crucial, conceptual switch from a dynamical gravitational field to a test field on a fixed background is often omitted in presenting this course material. This issue is clarified and an improved presentation is proposed.