It is well known that for a fermion system with an isotropic equation of state (EOS), the square of the speed of sound (SOS)2 is a measure of the stiffness of the equation of state (EOS). It is also known that in the presence of a magnetic field the EOS becomes anisotropic with two different pressures arising, one directed parallel to the field direction and one perpendicular to it. Since the SOS in a medium is created by pressure oscillations, the anisotropy in the pressure should be transferred to the SOS. In this paper, we derive from first principles the anisotropic wavelike equation from where the expressions for the longitudinal and transverse SOS in the presence of a uniform magnetic f ield can be obtained. We also investigate the degree to which the magnetic field in the weak and the strong limit affects the two SOS of (i) a system of hadrons modeled by the nonlinear Walecka model and (ii) a system of quarks modeled by the MIT bag model. We find that for the systems considered, the effects of the magnetic field on the SOS anisotropy are mild up to 1018G. Links to neutrons star physics are discussed throughout the paper.
Ferrer, E. J., and A. Hackebill. "Speed of Sound for Hadronic and Quark Phases in a Magnetic Field." arXiv preprint arXiv:2203.16576 (2022).