Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?

Abstract

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.

Comments: 10 pages, 3 figures, matches the published version. Essay received an Honorable Mention in the 2018 Essay Competition of the Gravity Research Foundation