Linear analysis of the Kelvin-Helmholtz instability in relativistic magnetized symmetric flows

Abstract We study the linear stability of a planar interface separating two fluids in relative motion, focusing on symmetric configuration where have same properties (density, temperature, magnetic field strength, and direction). consider most general case with arbitrary sound speed cs, Alfvén vA, orientation. For instability associated fast mode, we find that lower bound unstable shear velocities is set by requirement projection velocity onto fluid-frame wavevector larger than direction, i.e., should overcome effect tension. In frame move opposite directions equal v, upper corresponds to an effective relativistic Mach number $M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1-v_{\rm }^2)/(1-v^2)} \cos \theta =\sqrt{2}$, $v_{\rm }=[v_{\rm {A}}^2+c_{\rm s}^2(1-v_{\rm {A}}^2)]^{1/2}$ assuming perpendicular (here, all are units light), θ laboratory-frame angle between flow interface. Our results implications for flows magnetospheres neutron stars black holes — both single objects merging binaries may approach light.