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The Einstein field equations of gravitation are characterized by cross-scale,high-order nonlinear terms, representing a challenge for numerical modeling. Inan exact spectral decomposition, high-order nonlinearities correspond to aconvolution that numerically might lead to aliasing instabilities. We present astudy of this problem, in vacuum conditions, based on the $3+1$Baumgarte-Shibata-Shapiro-Nakamura (BSSN) formalism. We inspect the emergenceof numerical artifacts, in a variety of conditions, by using theSpectral-FIltered Numerical Gravity codE (\texttt{SFINGE}) - a pseudo-spectralalgorithm, based on a classical (Cartesian) Fourier decomposition. Bymonitoring the highest $k-$modes of the dynamical fields, we identify theculprits of the aliasing and propose procedures that cure such instabilities,based on the suppression of the aliased wavelengths. This simple algorithm,together with appropriate treatment of the boundary conditions, can be appliedto a variety of gravitational problems, including those related to massiveobjects dynamics.

Aliasing Instabilities in the Numerical Evolution of the Einstein Field Equations