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Alfvén wave collisions are the primary building blocks of the nonrelativistic turbulence that permeates the heliosphere and low to moderateenergy astrophysical systems. However, many astrophysical systems such as gammaray bursts, pulsar and magnetar magnetospheres and active galactic nuclei have relativistic flows or energy densities. To better understand these highenergy systems, we derive reduced relativistic magnetohydrodynamics equations and employ them to examine weak Alfvénic turbulence, dominated by threewave interactions, in reduced relativistic magnetohydrodynamics, including the forcefree, infinitely magnetized limit. We compare both numerical and analytical solutions to demonstrate that many of the findings from nonrelativistic weak turbulence are retained in relativistic systems. But, an important distinction in the relativistic limit is the inapplicability of a formally incompressible limit, i.e. there exists finite coupling to the compressible fast mode regardless of the strength of the magnetic field. Since fast modes can propagate across field lines, this mechanism provides a route for energy to escape strongly magnetized systems, e.g. magnetar magnetospheres. However, we find that the fastAlfvén coupling is diminished in the limit of oblique propagation.

Alfvén waves as excited in black hole accretion disks and neutron star magnetospheres are the building blocks of turbulence in relativistic, magnetized plasmas. A large reservoir of magnetic energy is available in these systems, such that the plasma can be heated significantly even in the weak turbulence regime. We perform highresolution threedimensional simulations of counterpropagating Alfvén waves, showing that an $E_{B_{\perp }}(k_{\perp }) \propto k_{\perp }^{2}$ energy spectrum develops as a result of the weak turbulence cascade in relativistic magnetohydrodynamics and its infinitely magnetized (forcefree) limit. The plasma turbulence ubiquitously generates current sheets, which act as locations where magnetic energy dissipates. We show that current sheets form as a natural result of nonlinear interactions between counterpropagating Alfvén waves. These current sheets form owing to the compression of elongated eddies, driven by the shear induced by growing higherorder modes, and undergo a thinning process until they breakup into smallscale turbulent structures. We explore the formation of current sheets both in overlapping waves and in localized wave packet collisions. The relativistic interaction of localized Alfvén waves induces both Alfvén waves and fast waves, and efficiently mediates the conversion and dissipation of electromagnetic energy in astrophysical systems. Plasma energization through reconnection in currentmore »