Related papers: Gauge conditions for long-term numerical black hol…

Recent demonstrations of unexcised black holes traversing across computational grids represent a significant advance in numerical relativity. Stable and accurate simulations of multiple orbits, and their radiated waves, result. This…

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…

We report new results which establish that the accurate 3-dimensional numerical simulation of generic single-black-hole spacetimes has been achieved by characteristic evolution with unlimited long term stability. Our results cover a…

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…

Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary…

We extend previous work on 3D black hole excision to the case of distorted black holes, with a variety of dynamic gauge conditions that are able to respond naturally to the spacetime dynamics. We show that the combination of excision and…

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…

We prove by explicit construction that there exists a maximal slicing of the Schwarzschild spacetime such that the lapse has zero gradient at the puncture. This boundary condition has been observed to hold in numerical evolutions, but in…

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this…

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.…

A paradigm deeply rooted in modern numerical relativity calculations prescribes the removal of those regions of the computational domain where a physical singularity may develop. We here challenge this paradigm by performing…

We evolve a scalar field in a fixed Kerr-Schild background geometry to test simple $(3+1)$-dimensional algorithms for singularity excision. We compare both centered and upwind schemes for handling the shift (advection) terms, as well as…

We present long-term stable and second-order convergent evolutions of an excised wobbling black hole. Our results clearly demonstrate that the use of a densitized lapse function extends the lifetime of simulations dramatically. We also show…

While numerous numerical relativity simulations adopt a 1+log slicing condition, shock-avoiding slicing conditions form a viable and sometimes advantageous alternative. Despite both conditions satisfying similar equations, recent numerical…

The family of generalized-harmonic gauge conditions, which is currently used in Numerical Relativity for its singularity-avoidant behavior, is analyzed by looking for pathologies of the corresponding spacetime foliation. The appearance of…

Spacetime singularities in numerical relativity can be avoided by excising a region of the computational domain from inside the apparent horizon. We report on results of such a scheme that is based on using ({\it i}) a horizon locking…

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial…

We present a singularity excision algorithm appropriate for numerical simulations of black holes moving throughout the computational domain. The method is an extension of the excision procedure previously used to obtain stable simulations…

When using black hole excision to numerically evolve a black hole spacetime with no continuous symmetries, most 3+1 finite differencing codes use a Cartesian grid. It's difficult to do excision on such a grid, because the natural $r =…

We perform both distorted black hole evolutions and binary black hole head on collisions and compare the results of using a full grid to results obtained by excising the black hole interiors. In both cases the evolutions are found to run…