Towards a singularity-proof scheme in numerical relativity

Seidel, Edward; Suen, Wai-Mo

doi:10.1103/physrevlett.69.1845

Cited by 137 publications

(225 citation statements)

References 8 publications

Supporting

Mentioning

221

Contrasting

Order By: Relevance

“…It may also require the use of an "horizon excision" boundary condition (W. Unruh 1984, unpublished;Thornburg 1987;Seidel & Suen 1992). To simultaneously follow the extended disk may necessitate employing a nested grid or adaptive mesh refinement.…”

Section: Discussionmentioning

confidence: 99%

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Fully Relativistic Simulations

Shibata

Shapiro

2002

The Astrophysical Journal

193

183

View full text Add to dashboard Cite

We follow the collapse in axisymmetry of a uniformly rotating, supermassive star (SMS) to a supermassive black hole in full general relativity. The initial SMS of arbitrary mass M is marginally unstable to radial collapse and rotates at the mass-shedding limit. The collapse proceeds homologously early on and results in the appearance of an apparent horizon at the center. Although our integration terminates before final equilibrium is achieved, we determine that the final black hole will contain about 90% of the total mass of the system and will have a spin parameter . The remaining gas forms a rotating disk about the nascent hole.

show abstract

Section: Discussionmentioning

confidence: 99%

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Fully Relativistic Simulations

Shibata

Shapiro

2002

The Astrophysical Journal

193

183

View full text Add to dashboard Cite

show abstract

“…In a recent paper [18] we demonstrated that a horizon boundary condition can be realized. Here we present a more detailed discussion of our methods and various extensions to that earlier work.…”

Section: Introductionmentioning

confidence: 99%

“…This amounts to using a shift vector that locks the horizon in place near a particular coordinate location, and also keeps other coordinate lines from drifting towards the hole. In [18] we investigated one particular type of shift condition, namely the "distance freezing" shift. Here we report on various choices of shift conditions, including the original "distance freezing" shift that freezes the proper distance to the horizon, an "expansion freezing" shift that freezes the rate of expansion of outgoing null rays, an "area freezing" shift that freezes the area of radial shells, and the minimal distortion shift [19] that minimizes the global distortion in the 3-metric.…”

Section: Introductionmentioning

confidence: 99%

Horizon boundary condition for black hole spacetimes

et al. 1995

Self Cite

View full text Add to dashboard Cite

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 scheme. The scheme is based on using (1) a horizon locking coordinate which locks the coordinate system to the geometry, and (2) a finite differencing scheme which respects the causal structure of the spacetime. We show that the horizon locking coordinate can be affected by a number of shift conditions, such as a "distance freezing" shift, an "area freezing" shift, an "expansion freezing" shift, or the minimal distortion shift. The causal differencing scheme is illustrated with the evolution of scalar fields, and its use in evolving the Einstein equations is studied. We compare the results of numerical evolutions with and without the use of this horizon boundary condition scheme for spherical black hole spacetimes. With the boundary condition a black hole can be evolved accurately well beyond t = 1000M , where M is the black hole mass.PACS numbers: 04.30.+x, 95.30.Sf, 04.25.Dm

show abstract

“…Current FD codes for evolving black hole spacetimes with excised horizons are mostly based on a numerical technique known as causal differencing [22][23][24][25][26][27], which allows one to update the fundamental variables in time while avoiding numerical problems associated with superluminal grid speeds. This technique has been used successfully to propagate an excised hole across a grid, even when grid points fall into or emerge from the horizon [25].…”

Section: Introductionmentioning

confidence: 99%

Black hole evolution by spectral methods

et al. 2000

View full text Add to dashboard Cite

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 differencing. In this paper, we explore the use of a pseudospectral collocation (PSC) method for the evolution of a spherically symmetric black hole spacetime in one dimension using a hyperbolic formulation of Einstein's equations. We demonstrate that our PSC method is able to evolve a spherically symmetric black hole spacetime forever without enforcing constraints, even if we add dynamics via a Klein-Gordon scalar field. We find that, in contrast to finite-differencing methods, black hole excision is a trivial operation using PSC applied to a hyperbolic formulation of Einstein's equations. We discuss the extension of this method to three spatial dimensions.04.25.Dm, 02.70.Hm

show abstract

Towards a singularity-proof scheme in numerical relativity

Cited by 137 publications

References 8 publications

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Fully Relativistic Simulations

Collapse of a Rotating Supermassive Star to a Supermassive Black Hole: Fully Relativistic Simulations

Horizon boundary condition for black hole spacetimes

Black hole evolution by spectral methods

Contact Info

Product

Resources

About