相关论文: Conservative Evolution of Black Hole Perturbations…

This is the second in a series of papers describing a 3+1 computational scheme for the numerical simulation of dynamic black hole spacetimes. We discuss the numerical time-evolution of a given black-hole-containing initial data slice in…

We intend to develop part of the theoretical tools needed for the detection of gravitational waves coming from the capture of a compact object, 1-100 solar masses, by a Supermassive Black Hole, up to a 10 billion solar masses, located at…

Solving the 4-d Einstein equations as evolution in time requires solving equations of two types: the four elliptic initial data (constraint) equations, followed by the six second order evolution equations. Analytically the constraint…

Numerical evolution of time-dependent differential equations via explicit Runge-Kutta or Taylor methods typically fails to preserve symmetries of a system. It is known that there exists no numerical integration method that in general…

The Kerr black hole is stationary and axisymmetric, which leads to conservation of energy and azimuthal angular momentum along the orbits of free test particles in its vicinity, but also to conservation laws for the evolution of continuum…

We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing…

Within the next decade the Laser Interferometer Space Antenna (LISA) is due to be launched, providing the opportunity to extract physics from stellar objects and systems, such as \textit{Extreme Mass Ratio Inspirals}, (EMRIs) otherwise…

In the harmonic description of general relativity, the principle part of Einstein's equations reduces to 10 curved space wave equations for the componenets of the space-time metric. We present theorems regarding the stability of several…

In this paper, a complete analysis of symmetries and conservation laws for the charged squashed Kaluza--Klein black hole spacetime in a Riemannian space is discussed. First, a comprehensive group analysis of the underlying space-time metric…

Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…

We have developed a numerical code to study the evolution of self-gravitating matter in dynamic black hole axisymmetric spacetimes in general relativity. The matter fields are evolved with a high-resolution shock-capturing scheme that uses…

Gravitational radiation and some global properties of spacetimes can only be unambiguously measured at future null infinity . This motivates the interest in reaching it within simulations of coalescing compact objects, whose waveforms are…

Three dimensional (3D) numerical evolutions of static black holes with excision are presented. These evolutions extend to about 8000M, where M is the mass of the black hole. This degree of stability is achieved by using growth-rate…

A numerical solution scheme for the Einstein field equations based on generalized harmonic coordinates is described, focusing on details not provided before in the literature and that are of particular relevance to the binary black hole…

We analyze the excision strategy for simulating black holes. The problem is modeled by the propagation of quasi-linear waves in a 1-dimensional spatial region with timelike outer boundary, spacelike inner boundary and a horizon in between.…

We consider the numerical evolution of dynamic black hole initial data sets with a full 3D, nonlinear evolution code. These data sets consist of single black holes distorted by strong gravitational waves, and mimic the late stages of…

This paper is concerned with the Einstein equations in axisymmetric vacuum spacetimes. We consider numerical evolution schemes that solve the constraint equations as well as elliptic gauge conditions at each time step. We examine two such…

We present long term evolutions of a single black hole of mass $M$ with the BSSN system using pseudospectral methods. For our simulations we use the SGRID code where the BSSN system is implemented in its standard second order in space form.…

The lack of a positive-definite and conserved energy is a serious obstacle in the black hole stability problem. In this work, we will show that there exists a positive-definite and conserved Hamiltonian energy for axially symmetric linear…

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…