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

TL;DR

This paper explores gravitational analogs of Friedel oscillations in higher-derivative and infinite-derivative gravity theories, revealing oscillatory energy density patterns around gravitational impurities linked to regularization and non-locality scales.

Contribution

It introduces the concept of gravitational Friedel oscillations in linearized higher-derivative and infinite-derivative gravity, connecting oscillation wavelengths to fundamental regularization scales.

Findings

Energy density exhibits oscillations to negative values around gravitational impurities.

Oscillation wavelength correlates with the regularization and non-locality scales.

Analogous to Friedel oscillations in condensed matter systems.

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.