  Fast reconnection operating in magnetically dominated plasmas is often
invoked in models for magnetar giant flares, for magnetic dissipation in pulsar
winds, or to explain the gamma-ray flares observed in the Crab nebula, hence
its investigation is of paramount importance in high-energy astrophysics. Here
we study, by means of two dimensional numerical simulations, the linear phase
and the subsequent nonlinear evolution of the tearing instability within the
framework of relativistic resistive magnetohydrodynamics, as appropriate in
situations where the Alfven velocity approaches the speed of light. It is found
that the linear phase of the instability closely matches the analysis in
classical MHD, where the growth rate scales with the Lundquist number S as
S^-1/2, with the only exception of an enhanced inertial term due to the thermal
and magnetic energy contributions. In addition, when thin current sheets of
inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal"
tearing regime is retrieved, with modes growing independently on S and
extremely fast, on only a few light crossing times of the sheet length. The
overall growth of fluctuations is seen to solely depend on the value of the
background Alfven velocity. In the fully nonlinear stage we observe an inverse
cascade towards the fundamental mode, with Petschek-type supersonic jets
propagating at the external Alfven speed from the X-point, and a fast
reconnection rate at the predicted value R~(ln S)^-1.
