相关论文: Robust evolution system for Numerical Relativity

A gravitational theory is formulated by considering the physical processes underlying relativistic dilation of time and contraction of space. It is shown that the point mass solution of general relativity's field equation - the…

We suggest that ``free evolution'' integration schemes for the Einstein equations (that do not enforce constraints) may contain exponentially growing modes that render them useless in numerical integrations of black hole spacetimes,…

We experiment with modifications of the BSSN form of the Einstein field equations (a reformulation of the ADM equations) and demonstrate how these modifications affect the stability of numerical black hole evolution calculations. We use…

This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…

We present first results obtained with a 3+1 dimensional adaptive mesh code in numerical general relativity. The adaptive mesh is used in conjunction with a standard ADM code for the evolution of a dynamically sliced Schwarzschild spacetime…

We describe early success in the evolution of binary black hole spacetimes with a numerical code based on a generalization of harmonic coordinates. Indications are that with sufficient resolution this scheme is capable of evolving binary…

We present a new evolution system for Einstein's field equations which is based on tetrad fields and conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost freedom in the choice of the…

We present a semi-analytical binary black hole (BBH) metric approximation that models the entire evolution of the system from inspiral to merger. The metric is constructed as a boosted Kerr-Schild superposition following post-Newtonian (PN)…

It is often the case in numerical relativity that schemes that are known to be convergent for well posed systems are used in evolutions of weakly hyperbolic (WH) formulations of Einstein's equations. Here we explicitly show that with…

The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…

The Bondi solution, which describes the radial inflow of a gas onto a non-rotating black hole, provides a powerful test for numerical relativistic codes. However, the Bondi solution is usually derived in Schwarzschild coordinates, which are…

The recent detections of gravitational waves from binary systems of black holes are in remarkable agreement with the predictions of General Relativity. In this pedagogical mini-review, I will go through the physics of the different phases…

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…

We present an implementation of the Schwarzschild orbit superposition method which can be used for constructing self-consistent equilibrium models of barred or non-barred disc galaxies, or of elliptical galaxies with figure rotation. This…

We present a new solution in Einstein's General Relativity representing a Schwarzschild black hole immersed in a rotating universe. Such a solution is constructed analytically by means of the last unexplored Lie point symmetry of the Ernst…

Since the breakthrough papers from 2005/2006, the field of numerical relativity has experienced a growth spurt that took the two-body problem in general relativity from the category of "really-hard-problems" to the realm of…

The description of a point mass in general relativity (GR) is given in the framework of the field formulation of GR where all the dynamical fields, including the gravitational field, are considered in a fixed background spacetime. With the…

The static vacuum spherically symmetric solutions in massive gravity are obtained both analytically and numerically. The solutions depend on two parameters (integration constants): the mass M (or, equivalently, the Schwarzschild radius),…

We discuss the possibility of a dimensional reduction of the Einstein equations in S3 black-hole lattices. It was reported in previous literature that the evolution of spaces containing curves of local, discrete rotational and reflection…

We study numerically the fully nonlinear gravitational collapse of a self-gravitating, minimally-coupled, massless scalar field in spherical symmetry. Our numerical code is based on double-null coordinates and on free evolution of the…