相关论文: Conformal and covariant formulation of the Z4 syst…

Following previous work in vacuum spacetimes, we investigate the constraint-damping properties in the presence of matter of the recently developed traceless, conformal and covariant Z4 (CCZ4) formulation of the Einstein equations. First, we…

We show that by adding suitable lower-order terms to the Z4 formulation of the Einstein equations, all constraint violations except constant modes are damped. This makes the Z4 formulation a particularly simple example of a lambda-system as…

We compare numerical evolutions performed with the BSSNOK formulation and a conformal decomposition of a Z4-like formulation of General Relativity. The important difference between the two formulations is that the Z4 formulation has a…

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the…

We adopt a reference-metric approach to generalize a covariant and conformal version of the Z4 system of the Einstein equations. We refer to the resulting system as ``fully covariant and conformal", or fCCZ4 for short, since it is well…

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to…

We propose a re-formulation of the Einstein evolution equations that cleanly separates the conformal degrees of freedom and the non-conformal degrees of freedom with the latter satisfying a first order strongly hyperbolic system. The…

We study the constraint equations for the Einstein-scalar field system on compact manifolds. Using the conformal method we reformulate these equations as a determined system of nonlinear partial differential equations. By introducing a new…

One method of studying the asymptotic structure of spacetime is to apply Penrose's conformal rescaling technique. In this setting, the Einstein equations for the metric and the conformal factor in the unphysical spacetime degenerate where…

A new representation of the Einstein evolution equations is presented that is first order, linearly degenerate, and symmetric hyperbolic. This new system uses the generalized harmonic method to specify the coordinates, and exponentially…

We study numerical stability of different approaches to the discretization of a conformal decomposition of the Z4 formulation of general relativity. We demonstrate that in the linear, constant coefficient regime a novel discretization for…

One possibility for avoiding constraint violation in numerical relativity simulations adopting free-evolution schemes is to modify the continuum evolution equations so that constraint violations are damped away. Gundlach et. al.…

Shibata, Ury\=u and Friedman recently suggested a new decomposition of Einstein's equations that is useful for constructing initial data. In contrast to previous decompositions, the conformal metric is no longer treated as a…

We introduce a proposal to modify Einstein's equations by embedding them in a larger symmetric hyperbolic system. The additional dynamical variables of the modified system are essentially first integrals of the original constraints. The…

In this short note, we give a construction of solutions to the Einstein constraint equations using the well known conformal method. Our method gives a result similar to the one in [15, 16, 24], namely existence when the so called TT-tensor…

Bonazzola, Gourgoulhon, Grandcl\'ement, and Novak [Phys. Rev. D {\bf 70}, 104007 (2004)] proposed a new formulation for 3+1 numerical relativity. Einstein equations result, according to that formalism, in a coupled elliptic-hyperbolic…

The Einstein-Bianchi system uses symmetric and traceless tensors to reformulate Einstein's original field equations. However, preserving these algebraic constraints simultaneously remains a challenge for numerical methods. This paper…

We extend the conformal gluing construction of Isenberg-Mazzeo-Pollack [18] by establishing an analogous gluing result for field theories obtained by minimally coupling Einstein's gravitational theory with matter fields. We treat classical…

Inspired by a similar analysis for the vacuum conformal Einstein field equations by Paetz [Ann. H. Poincar\'e 16, 2059 (2015)], in this article we show how to construct a system of quasilinear wave equations for the geometric fields…

A new technique is presented for modifying the Einstein evolution equations off the constraint hypersurface. With this approach the evolution equations for the constraints can be specified freely. The equations of motion for the…