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.

arXiv comment10 pages, 3 figures, matches the published version. Essay received an Honorable Mention in the 2018 Essay Competition of the Gravity Research Foundation

References in corpus (17)

• Towards singularity and ghost free theories of gravity
• Super-renormalizable Quantum Gravity
• Super-renormalizable or Finite Lee-Wick Quantum Gravity
• Ghost-free infinite derivative quantum field theory
• Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity
• A formal framework for a nonlocal generalization of Einstein's theory of gravitation
• Counting ghosts in the "ghost-free" non-local gravity
• Head-on collision of ultrarelativistic particles in ghost-free theories of gravity
• Low-energy effects in a higher-derivative gravity model with real and complex massive poles
• The gravitational field of static p-branes in linearized ghost-free gravity
• On the cancellation of Newtonian singularities in higher-derivative gravity
• On the gravitational seesaw in higher-derivative gravity
• Sub-millimeter Spatial Oscillations of Newton's Constant: Theoretical Models and Laboratory Tests
• Non-perturbative spectrum of non-local gravity
• High-Energy Scatterings in Infinite-Derivative Field Theory and Ghost-Free Gravity
• Radiation from an emitter in the ghost free scalar theory
• Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity

Cited by in corpus (18)

• Characterizing black hole metrics in quadratic gravity
• Effective delta sources and regularity in higher-derivative and ghost-free gravity
• Weak-field limit and regular solutions in polynomial higher-derivative gravities
• $pp$-waves as exact solutions to ghost-free infinite derivative gravity
• Higher-order regularity in local and nonlocal quantum gravity
• Probing the vacuum fluctuations in scalar ghost-free theories
• Angle deficit & non-local gravitoelectromagnetism around a slowly spinning cosmic string
• Light bending by a slowly rotating source in quadratic theories of gravity
• A Unified Spectral Approach for Quasinormal Modes of Lee-Wick Black Holes
• Two approaches that prove divergence free nature of non-local gravity
• Regular multi-horizon Lee-Wick black holes
• Regular black holes from higher-derivative effective delta sources
• Fate of the false vacuum in string-inspired nonlocal field theory
• Gravitational radiation in Infinite Derivative Gravity and connections to Effective Quantum Gravity
• Black holes in non-local gravity
• Gravitational field of scalar lumps in higher-derivative gravity
• Solving the nonlinear biharmonic equation by the Laplace-Adomian and Adomian Decomposition Methods
• Renormalisable Non-local Quark-Gluon Interaction: Mass Gap, Chiral Symmetry Breaking & Scale Invariance