## Abstract

By studying, within the relativistic framework, the propagation of so-called infinitesimal discontinuities throughout a magnetized elastic perfect conductor in an initial state of high hydrostatic pressure $p_{0}$ and in the presence of a magnetic field of arbitrary strength, it is proven that there hold universal relations (i.e., that do not depend on the exact equation of state of the body) between the speeds [Note: See the image of page 537 for this formatted text.]$u_{\text{f}}$ and $u_{\text{s}}$ of so-called fast and slow magnetoelastic modes. These results, which should hold true in the crust of dense magnetic stars, have the following form. If [Note: See the image of page 537 for this formatted text.]$A_{0}$ is the relativistic Alfven number of the initial state and $a_{0}$ is the sound speed of a fictitious relativistic perfect fluid whose law of compression would yield the initial pressure $p_{0}$, then (with nondimensional speeds) [Note: See the image of page 537 for this formatted text.]$u_{\text{f}}^{2}=\frac{4}{3}[u_{\text{s}}^{2}(1+A_{0}^{2})]+(a_{0}^{2}-\frac{4}{3}A_{0}^{2})$ for a propagation along the magnetic field and [Note: See the image of page 537 for this formatted text.]$u_{\text{f}}^{2}(1+A_{0}^{2})=\frac{4}{3}u_{\text{s}}^{2}+(a_{0}^{2}+A_{0}^{2})$ for a propagation in a direction orthogonal to the magnetic field. These results generalize previous results obtained in relativistic elasticity by Carter and Maugin.