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Aliasing instabilities in the numerical evolution of the Einstein field equations


The Einstein field equations of gravitation are characterized by cross-scale, high-order nonlinear terms, representing a challenge for numerical modeling. In an exact spectral decomposition, high-order nonlinearities correspond to a convolution that numerically might lead to aliasing instabilities. We present a study of this problem, in vacuum conditions, based on the \(3+1\) Baumgarte–Shibata–Shapiro–Nakamura (BSSN) formalism. We inspect the emergence of numerical artifacts, in a variety of conditions, by using the Spectral-FIltered Numerical Gravity codE (SFINGE)—a pseudo-spectral algorithm, based on a classical (Cartesian) Fourier decomposition. By monitoring the highest \(k-\)modes of the dynamical fields, we identify the culprits 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 applied to a variety of gravitational problems, including those related to massive objects dynamics.

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The simulations have been performed at the Newton HPCC Computing Facility, at the University of Calabria.

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Meringolo, C., Servidio, S. Aliasing instabilities in the numerical evolution of the Einstein field equations. Gen Relativ Gravit 53, 95 (2021).

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  • Numerical relativity
  • Gravitational testbeds
  • BSSN decomposition
  • Black hole dynamics