  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 $\rho \equiv G{}_{\mu\nu}\xi{}^\mu \xi{}^\nu$ (with $\xi=\partial_t$)
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.
