相关论文: RCCZ4: A Reference Metric Approach to Z4
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…
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 report on the potential occurrence of a numerical instability in the long-time simulation of black holes using the Baumgarte-Shapiro-Shibata-Nakamura formulation of numerical relativity, even in the simple set-up of a Schwarzschild black…
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…
Recent developments in the modified harmonic and modified puncture gauges have opened new possibilities for performing stable numerical evolutions beyond General Relativity. In this work, we utilise techniques developed in the…
The development of hyperbolic formulations of Einstein's equations has revolutionized our ability to perform long-time, stable, accurate numerical simulations of strong field gravitational phenomena. However, hyperbolic methods have seen…
The parabolic-hyperbolic form of the constraints is integrated numerically. The applied numerical stencil is $4^{th}$ order accurate (in the spatial directions) while 'time'-integration is made by using the method of lines with a $4^{th}$…
The Rezzolla-Zhidenko (RZ) framework provides an efficient approach to characterize spherically symmetric black-hole spacetimes in arbitrary metric theories of gravity using a small number of variables [L. Rezzolla and A. Zhidenko, Phys.…
We discuss static spherically symmetric metrics which represent non-singular black holes in four- and higher-dimensional spacetime. We impose a set of restrictions, such as a regularity of the metric at the center $r=0$ and Schwarzschild…
A covariant, scalar-tensor gravity is constructed such that the static, spherically symmetric Rezzolla-Zhidenko metric is an exact solution to the theory. The equations describing gravitational perturbations of this spacetime, which…
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 Fully Constrained Formulation (FCF) of General Relativity is a novel framework introduced as an alternative to the hyperbolic formulations traditionally used in numerical relativity. The FCF equations form a hybrid elliptic-hyperbolic…
In order to perform accurate and stable long-term numerical integration of the Einstein equations, several hyperbolic systems have been proposed. We here report our numerical comparisons between weakly hyperbolic, strongly hyperbolic, and…
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…
This contribution summarizes the recent work carried out to analyze the behavior of the hyperbolic sector of the Fully Constrained Formulation (FCF) derived in Bonazzola et al. 2004. The numerical experiments presented here allows one to be…
We calculate the gravitational perturbations produced by a small mass in eccentric orbit about a much more massive Schwarzschild black hole and use the numerically computed perturbations to solve for the metric. The calculations are…
In this work, we analyze the strong lensing phenomenon and quasinormal modes (QNMs) in the case of black holes (BHs) surrounded by fluids within the framework of $f(R,T)$ gravity, adopting a minimally coupled model of the theory. Our…
We construct a numerical relativity code based on the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation for the gravitational quadratic $f(R)$ Starobinsky model. By removing the assumption that the determinant of the conformal 3-metric…
We consider unconstrained evolution schemes for the hyperboloidal initial value problem in numerical relativity as a promising candidate for the optimally efficient numerical treatment of radiating compact objects. Here, spherical symmetry…
We study asymptotically constrained systems for numerical integration of the Einstein equations, which are intended to be robust against perturbative errors for the free evolution of the initial data. First, we examine the previously…