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arXiv · 1804.00225

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

Jens Boos
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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 $ρ\equiv G{}_{μν}ξ^μξ^ν$ (with $ξ=\partial_t$) 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.

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Jens Boos. 2018-10-18. Gravitational Friedel oscillations in higher-derivative and infinite-derivative gravity?. https://doi.org/10.1142/s0218271818470223

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