Late time analysis for maximal slicing of Reissner-Nordström puncture evolutions

Reimann, Bernd; Bruegmann, Bernd

doi:10.1103/physrevd.69.124009

Cited by 13 publications

(55 citation statements)

References 23 publications

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“…In a numerical code we prefer to use a lapse that is always positive, or at least non-negative. Unfortunately, it is not possible to construct a time-independent, maximal slice of Schwarzschild with two asymptotically flat ends and an everywhere non-negative lapse, no matter what shift conditions we employ [55][56][57]. Put another way, a maximal-or 1 þ log-slicing evolution with two asymptotically flat ends and with a non-negative lapse cannot reach a stationary state.…”

Section: B Wormhole Puncture Data For a Schwarzschild Black Holementioning

confidence: 99%

Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation

Hannam

Husa

Ohme³

et al. 2008

Phys. Rev. D

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121

241

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Original citationHannam, M., Husa, S., Ohme, F., Brügmann, B. and Ó Murchadha, N. We expand upon our previous analysis of numerical moving-puncture simulations of the Schwarzschild spacetime. We present a derivation of the family of analytic stationary 1 þ log foliations of the Schwarzschild solution, and outline a transformation to isotropic coordinates. We discuss in detail the numerical evolution of standard Schwarzschild puncture data, and the new time-independent 1 þ log data. Finally, we demonstrate that the moving-puncture method can locate the appropriate stationary geometry in a robust manner when a numerical code alternates between two forms of 1 þ log slicing during a simulation.

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Section: B Wormhole Puncture Data For a Schwarzschild Black Holementioning

confidence: 99%

Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation

Hannam

Husa

Ohme³

et al. 2008

Phys. Rev. D

Self Cite

121

241

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show abstract

“…For those foliations it is hence possible to examine slice stretching on an analytic level, and compare the effects with those arising for other slicings such as geodesic slicing [30]. The discussion throughout this paper is restricted to Schwarzschild, but since the same notation as in [4][5][6] is used, the results carry over in a straightforward way to Reissner-Nordström.…”

Section: Introductionmentioning

confidence: 99%

“…Following up on earlier work done together with Brügmann, [4][5][6], in the present paper one particular singularity avoiding slicing is looked at, namely maximal slicing corresponding to the condition that the mean extrinsic curvature of the slices vanishes at all times [7]. This geometrically motivated choice of the lapse function has been used frequently in numerical relativity (for simulations of a single Schwarzschild black hole see e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Performing a late time analysis as in [6] based on [17], it is shown then that slice stretching arises at the throat of the Einstein-Rosen bridge [18].…”

Section: Introductionmentioning

confidence: 99%

“…Examples of spatial coordinates to be discussed in the context of even boundary conditions are logarithmic grid coordinates (explaining numerical observations of e.g. [9,11]) and isotropic grid coordinates (extending the study of [6]). …”

Section: Introductionmentioning

confidence: 99%

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Slice stretching effects for maximal slicing of a Schwarzschild black hole

Reimann

2005

Class. Quantum Grav.

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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 are quantified here in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favourable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding, however, that a numerically favourable lapse remains non-negative, as a result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.

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Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity

Bona

Alic

2008

EAS Publications Series

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The harmonic formulation of Einstein's field equations is considered, where the gauge conditions are introduced as dynamical constraints. The difference between the fully constrained approach (used in analytical approximations) and the free evolution one (used in most numerical approximations) is pointed out. As a generalization, quasi-stationary gauge conditions are also discussed, including numerical experiments with the gauge-waves testbed. The complementary 3+1 approach is also considered, where constraints are related instead with energy and momentum first integrals and the gauge must be provided separately. The relationship between the two formalisms is discussed in a more general framework (Z4 formalism). Different strategies in black hole simulations follow when introducing singularity avoidance as a requirement. More flexible quasi-stationary gauge conditions are proposed in this context, which can be seen as generalizations of the current 'freezing shift' prescriptions

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Late time analysis for maximal slicing of Reissner-Nordström puncture evolutions

Abstract: Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally, a derivation of Newtonian Gravity from Einstein's Equations is given.

Cited by 13 publications

References 23 publications

Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation

Wormholes and trumpets: Schwarzschild spacetime for the moving-puncture generation

Slice stretching effects for maximal slicing of a Schwarzschild black hole

Gauge and constraint degrees of freedom: from analytical to numerical approximations in General Relativity

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