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When magnetic energy density is much larger than that of matter, as inpulsar/black hole magnetospheres, the medium becomes force-free and we needrelativity to describe it. As in non-relativistic magnetohydrodynamics (MHD),Alfv\'enic MHD turbulence in the relativistic limit can be described byinteractions of counter-traveling wave packets. In this paper we numericallystudy strong imbalanced MHD turbulence in such environments. Here, imbalancedturbulence means the waves traveling in one direction (dominant waves) havehigher amplitudes than the opposite-traveling waves (sub-dominant waves). Wefind that (1) spectrum of the dominant waves is steeper than that ofsub-dominant waves, (2) the anisotropy of the dominant waves is weaker thanthat of sub-dominant waves, and (3) the dependence of the ratio of magneticenergy densities of dominant and sub-dominant waves on the ratio of energyinjection rates is steeper than quadratic (i.e., \$b_+^2/b_-^2 \propto(\epsilon_+/\epsilon_-)^n \$ with n>2). These results are consistent with thoseobtained for imbalanced non-relativistic Alfv\'enic turbulence. Thiscorresponds well to the earlier reported similarity of the relativistic andnon-relativistic balanced magnetic turbulence.

Imbalanced Relativistic Force-Free Magnetohydrodynamic Turbulence