Relativistic magnetic reconnection at X-type neutral points

Relativistic effects in the oscillatory damping of magnetic disturbances near two-dimensional X-points are investigated. By taking into account displacement current, we study new features of extremely magnetized systems, in which the Alfv\'en velocity is almost the speed of light. The frequencies of the least-damped mode are calculated using linearized relativistic MHD equations for wide ranges of the Lundquist number S and the magnetization parameter $\sigma$. These timescales approach constant values in the large resistive limit: the oscillation time becomes a few times the light crossing time, irrespective of $\sigma$, and the decay time is proportional to $\sigma$ and therefore is longer for a highly magnetized system.