hide
Free keywords:
General Relativity and Quantum Cosmology, gr-qc
Abstract:
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 constraint-damped 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.