Dipolar stellar oscillations in general relativity

We have obtained a concise second-order system of equations that describes the adiabatic dipolar oscillation of stars in general relativity, rather than the third-order system which is conventionally used. The new system is derived by utilizing a known algebraic relation, which reduces to the integral of momentum conservation in the Newtonian limit, and by formulating the problem as a Hamiltonian system. The thus-derived system enables us to classify the relativistic dipolar modes unambiguously. We find that there is essentially little difference in the properties of the dipolar stellar oscillation between the general-relativistic case and the Newtonian case.