The main goal of this thesis is the study of magnetic reconnection in relativistic plasma of astrophysical interest. We pay special attention to the dynamical effects that the resistive dissipation of magnetic fields may have in such process. Thus, our approach to the study is numerical, i.e. we developed numerical models that mimic as closely as possible the physical conditionsunder which reconnection happens in relativistic astrophysical plasma. The goals of this thesis can be grouped in two sets: computational and physical. Considering that we aim to obtain physical results (ideally) indepen-dent of the numerical methods that we employ, we pursue the development of a new multidimensional RRMHD code for astrophysical applications. The code include, different numerical algorithms for the time-evolution, for the solution of the Riemann problem and for the intercell reconstruction. Only in this way we may calibrate the impact of the numerical methods on the results. Therefore, concerning the physics of reconnection in astro-physical plasma, our first and foremost goal is to understand the dependenceof the growth rate of resistive instabilities (such as TM instabilities) on the physical properties of the plasma. We shall consider specifically the case of relativistic ideal double tearing modes (RIDTMs), where the adjective ideal refers to the fact that the instability develops at a timescale of the order of the MHD timescale (i.e. Alfvén crossing time) and its growth rate is independent of the resistivity (and thus, it does not diverge in the ideal RMHD regime). This is an unexplored and interesting setup where two parallel current sheets may interact as TMs develop yielding an explosive reconnection episode, where the reconnection time scales are so small that may be of interest for explaining a number of astrophysical objects.
