When a positively charged impurity is placed inside a cold metal, the resulting charge density around that object exhibits characteristic ripples to negative values, known as Friedel oscillations. In this essay, we describe a somewhat analogous effect in (i) linearized higher-derivative gravity and (ii) linearized infinite-derivative "ghost-free" gravity: when a gravitational impurity (point particle) is placed in Minkowski vacuum, the local energy density ρ ≡ G µν ξ µ ξ ν (with ξ = ∂ t ) exhibits oscillations to negative values. The wavelength of these oscillations is roughly given by (i) the Pauli-Villars regularization scale and (ii) the scale of non-locality. We hence dub this phenomenon gravitational Friedel oscillations.file: gravitational-friedel-oscillations-v6.tex, Oct