Maximal foliations of extended Schwarzschild space

Reinhart, Bruce L.

doi:10.1063/1.1666384

Cited by 60 publications

(46 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So far these solutions depend on all four parameters M SH , W , r BH , and r SH . We now find a relation between these parameters by inserting (A2) and (A3) into the geodesic equation (23), which yields…”

Section: Discussionmentioning

confidence: 99%

“…The former is a transformation of Kerr-Schild (Eddington-Finkelstein) coordinates to isotropic coordinates, keeping the same time slicing, which we can produce by choosing K = K KS and α AH = 1/ √ 2 in our code. The latter is an isotropic representation of a maximal slice (with the critical parameter C = 3 √ 3M 2 /4, see [22,23]), which has recently attracted interest as an analytic "puncture" solution (compare [24]). We can produce this solution by choosing K = K MS = 0 and α AH = 3 √ 3/16 in our code.…”

Section: B Testsmentioning

confidence: 99%

See 1 more Smart Citation

Shells around black holes: The effect of freely specifiable quantities in Einstein’s constraint equations

Matera¹,

Baumgarte²,

Gourgoulhon³

2008

Phys. Rev. D

View full text Add to dashboard Cite

We solve Einstein's constraint equations in the conformal thin-sandwich decomposition to model thin shells of non-interacting particles in circular orbit about a non-rotating black hole. We use these simple models to explore the effects of some of the freely specifiable quantities in this decomposition on the physical content of the solutions. Specifically, we adopt either maximal slicing or Kerr-Schild slicing, and make different choices for the value of the lapse on the black hole horizon. For one particular choice of these quantities the resulting equations can be solved analytically; for all others we construct numerical solutions. We find that these different choices have no effect on our solutions when they are expressed in terms of gauge-invariant quantities.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: B Testsmentioning

confidence: 99%

Shells around black holes: The effect of freely specifiable quantities in Einstein’s constraint equations

Matera¹,

Baumgarte²,

Gourgoulhon³

2008

Phys. Rev. D

View full text Add to dashboard Cite

show abstract

“…as t → ∞ See also the earlier works by Estabrook and others [22,25,26,27]. This gives us another test where a plot of ln N versus t should be a straight line.…”

Section: Collapse Of the Lapsementioning

confidence: 99%

Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

Brewin

2002

Class. Quantum Grav.

View full text Add to dashboard Cite

We will present results of a numerical integration of a maximally sliced Schwarzschild black hole using a smooth lattice method. The results show no signs of any instability forming during the evolutions to t = 1000m. The principle features of our method are i) the use of a lattice to record the geometry, ii) the use of local Riemann normal coordinates to apply the 1+1 ADM equations to the lattice and iii) the use of the Bianchi identities to assist in the computation of the curvatures. No other special techniques are used. The evolution is unconstrained and the ADM equations are used in their standard form.

show abstract

“…(51) is degenerate and leads to an ill-posed elliptic system. We can understand the nature of the degeneracy by considering the family of timeindependent maximal slicings of Schwarzschild [23,24,25]. The line element for the spatial metric, lapse, and shift vector are…”

Section: Boundary Conditions On the Lapse Functionmentioning

confidence: 99%

Excision boundary conditions for black-hole initial data

2004

View full text Add to dashboard Cite

We define and extensively test a set of boundary conditions that can be applied at black hole excision surfaces when the Hamiltonian and momentum constraints of general relativity are solved within the conformal thin-sandwich formalism. These boundary conditions have been designed to result in black holes that are in quasiequilibrium and are completely general in the sense that they can be applied with any conformal three-geometry and slicing condition. Furthermore, we show that they retain precisely the freedom to specify an arbitrary spin on each black hole. Interestingly, we have been unable to find a boundary condition on the lapse that can be derived from a quasiequilibrium condition. Rather, we find evidence that the lapse boundary condition is part of the initial temporal gauge choice. To test these boundary conditions, we have extensively explored the case of a single black hole and the case of a binary system of equal-mass black holes, including the computation of quasi-circular orbits and the determination of the inner-most stable circular orbit. Our tests show that the boundary conditions work well.

show abstract

Maximal foliations of extended Schwarzschild space

Abstract: Smooth families of spherically symmetric maximal surfaces which are spacelike except at r = 2m are explicitly constructed in Schwarzschild space. Such surfaces should be useful in the study of initial value problems.

Cited by 60 publications

References 2 publications

Shells around black holes: The effect of freely specifiable quantities in Einstein’s constraint equations

Shells around black holes: The effect of freely specifiable quantities in Einstein’s constraint equations

Long term stable integration of a maximally sliced Schwarzschild black hole using a smooth lattice method

Excision boundary conditions for black-hole initial data

Contact Info

Product

Resources

About