Conformal and covariant formulation of the Z4 system with constraint-violation damping

By D. Alic, Carles Bona-Casas, C. Bona, Luciano Rezzolla, Carlos Palenzuela. 2011

171 citations recorded by the source corpus.

We present a new formulation of the Einstein equations based on a conformal and traceless decomposition of the covariant form of the Z4 system. This formulation combines the advantages of a conformal decomposition, such as the one used in the BSSNOK formulation (i.e. well-tested hyperbolic gauges, no need for excision, robustness to imperfect boundary conditions) with the advantages of a constraintdamped formulation, such as the generalized harmonic one (i.e. exponential decay of constraint violations when these are produced). We validate the new set of equations through standard tests and by evolving binary black hole systems. Overall, the new conformal formulation leads to a better behavior of the constraint equations and a rapid suppression of the violations when they occur. The changes necessary to implement the new conformal formulation in standard BSSNOK codes are very small as are the additional computational costs.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/0496f8999e14483895779ad85fb368dcbd6ebb37

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Citations in the corpus

GRChombo: Numerical relativity with adaptive mesh refinement (2015, methodology): “As was shown in [29] stability can be achieved by adding in the CCZ4 constraint damping terms GRChombo shows exactly this behaviour (figure 15).”
Dynamical Mass Ejection from Binary Neutron Star Mergers (2016, background): “Alternatively, the errors in the constraint could be mitigated adopting constraint-damping formulations of the Einstein equations (Bernuzzi & Hilditch 2010; Weyhausen et al. 2012; Alic et al. 2012; Hilditch et al. 2013; Alic et al. 2013; Kastaun et al. 2013).”