Related papers: Stability of the puncture method with a generalize…
Many of the recent numerical simulations of binary black holes in vacuum adopt the moving puncture approach. This successful approach avoids the need to impose numerical excision of the black hole interior and is easy to implement. Here we…
Excision techniques are used in order to deal with black holes in numerical simulations of Einstein equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead…
Approximate solutions to the Einstein field equations are a valuable tool to investigate gravitational phenomena. An important aspect of any approximation is to investigate and quantify its regime of validity. We present a study that…
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…
The aim of this paper is to study the stability of soliton-like static solutions via non-linear simulations in the context of a special class of massive tensor-multi-scalar-theories of gravity whose target space metric admits Killing…
The ``moving puncture'' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et.al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving puncture…
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…
Relativistic simulations in 3+1 dimensions typically monitor the Hamiltonian and momentum constraints during evolution, with significant violations of these constraints indicating the presence of instabilities. In this paper we rewrite the…
We discuss an equivalence between the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein evolution equations, a subfamiliy of the Kidder--Scheel--Teukolsky formulation, and other strongly or symmetric hyperbolic first…
Standard puncture initial data have been widely used for numerical binary black hole evolutions despite their shortcomings, most notably the inherent lack of gravitational radiation at the initial time that is later followed by a burst of…
We show a stability result for the Schwarzschild singularity (inside the black hole region) for the Einstein vacuum equations. The result is proven in the class of polarized axial symmetry, under perturbations of the Schwarzschild data…
The numerical evolution of Einstein's field equations in a generic background has the potential to answer a variety of important questions in physics: from applications to the gauge-gravity duality, to modelling black hole production in TeV…
In this study, we investigate the numerical stability of the covariant Baumgarte--Shapiro--Shibata--Nakamura (cBSSN) formulation against the Friedmann--Lema\^itre--Robertson--Walker spacetime. To evaluate the numerical stability, we…
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…
When simulating the inspiral and coalescence of a binary black-hole system, special care needs to be taken in handling the singularities. Two main techniques are used in numerical-relativity simulations: A first and more traditional one…
We review in generality why time-independent endstates can be reached in black hole and collapse simulations, with and without excision. We characterise the Killing states of the Bona-Masso slicing condition with time derivative along the…
Current methods of evolving a spacetime containing one or more black holes are plagued by instabilities that prohibit long-term evolution. Some of these instabilities may be due to the numerical method used, traditionally finite…
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…
We extend a recently developed numerical code to obtain stationary, axisymmetric solutions that describe rotating black hole spacetimes in a wide class of modified theories of gravity. The code utilizes a relaxed Newton-Raphson method to…
Though loop quantization of several spacetimes has exhibited existence of a bounce via an explicit evolution of states using numerical simulations, the question about the way central singularity is resolved in the black hole interior has…