Wave Packets in Curved Space: Curvature-Field Coupling

TL;DR

This paper develops an analytical framework for elastic wave propagation on curved manifolds with non-zero scalar curvature, providing new insights and testing its accuracy through specific cases.

Contribution

It introduces a novel analytical approach to model elastic waves on curved spaces, extending wave theory beyond flat geometries.

Findings

Method accurately solves wave equations on curved manifolds.

Curvature influences wave behavior and physical insights.

Framework applicable to arbitrary Riemannian manifolds.

Abstract

Elastic wave propagation is a century-old problem. Unlike on a flat manifold, analytical solution is not well established for a curved manifold. In this study we take a step towards building an analytical framework for solving the elastic wave propagation problem on an arbitrary manifold which admits a Riemannian metric with a global non-zero scalar curvature. We demonstrate the accuracy of the method by solving for some test cases, and also discuss some interesting physical insight that comes from solving the wave equations for non-vanishing curvature.