(3 + 1)-formulation for gravity with torsion and non-metricity: II. The hypermomentum equation

In this article, we consider a special case of Metric-Affine f(R)-gravity for f(R) = R, i.e. the General Relativity (MAGR). As companion to first article in series, perform (3+1) decomposition hypermomentum equation, obtained from minimization MAGR action S [g, {\omega}] with respect connection {\omega}. Moreover, show that tensor H could be constructed completely 10 hypersurfaces variables arise its dilation, shear, and rotational (spin) parts. The equations consists 1 scalar, 3 vector, matrix, equation order-(2,1). Together traceless torsion constraint, consisting scalar vector obtain hypersurface equations, which are main result article. Finally, some cases MAGR, namely, zero hypermomentum, metric, torsionless cases. For vanishing retrieve metric compatibility condition framework, hence forcing affine Levi-Civita as standard Relativity.