Coupled Oscillator Model for Nonlinear Gravitational Perturbations

TL;DR

This paper introduces a novel oscillator-based formalism to analyze nonlinear gravitational perturbations, linking Einstein equations to coupled harmonic oscillators, with applications demonstrated in asymptotically anti-de Sitter black brane spacetimes.

Contribution

The paper develops a new method mapping nonlinear Einstein equations to coupled oscillators, extending the gravity/fluid correspondence to more general spacetimes.

Findings

Validated the oscillator formalism with AdS black brane perturbations

Established equivalence between boundary fluid dynamics and bulk quasinormal modes

Proposed wider applicability beyond fluid dual spacetimes

Abstract

Motivated by the gravity/fluid correspondence, we introduce a new method for characterizing nonlinear gravitational interactions. Namely we map the nonlinear perturbative form of the Einstein equation to the equations of motion of a collection of nonlinearly-coupled harmonic oscillators. These oscillators correspond to the quasinormal or normal modes of the background spacetime. We demonstrate the mechanics and the utility of this formalism within the context of perturbed asymptotically anti-de Sitter black brane spacetimes. We confirm in this case that the boundary fluid dynamics are equivalent to those of the hydrodynamic quasinormal modes of the bulk spacetime. We expect this formalism to remain valid in more general spacetimes, including those without a fluid dual. In other words, although borne out of the gravity/fluid correspondence, the formalism is fully independent and it has a much wider range of applicability. In particular, as this formalism inspires an especially transparent physical intuition, we expect its introduction to simplify the often highly technical analytical exploration of nonlinear gravitational dynamics.