General-relativistic perturbation equations for the dynamics of elastic deformable astronomical bodies expanded in terms of generalized spherical harmonics

TL;DR

This paper derives general relativistic perturbation equations for elastic astronomical bodies using generalized spherical harmonics, simplifying complex PDEs into ODEs for improved numerical modeling of planetary dynamics.

Contribution

It extends previous work by expanding the relativistic perturbation equations in terms of generalized spherical harmonics, facilitating numerical simulations of elastic celestial bodies.

Findings

Equations are expressed as ordinary differential equations.

The approach simplifies the analysis of global planetary dynamics.

Potential applications in numerical modeling of Earth's behavior.

Abstract

In our previous paper, based on the Carter & Quintana framework and the Damour-Soffel-Xu scheme, we deduced a complete and closed set of post-Newtonian dynamical equations for elastically deformable astronomical bodies. In this paper, we expand the general relativistic perturbation equations of elastic deformable bodies (field equations, stress-strain relation, Euler equation) in terms of Generalized Spherical Harmonics. This turns the set of complicated partial differential equations into a set of ordinary differential equations. This will be useful for numerical applications that mainly deal with the global dynamics of the Earth.