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

Hannam, M. D.; Husa, S.; Ohme, F.; Brügmann, Bernd; Murchadha, Niall Ó

doi:10.1103/physrevd.78.064020

Cited by 121 publications

(255 citation statements)

References 85 publications

(145 reference statements)

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“…ϕ ∼ 1/ √ r, and the late-time behavior of the determinant of the 3-metric for a Schwarzschild black hole [87,88,89,90] with the standard moving-puncture choice for the gauge Eqs. (30).…”

Section: Discussionmentioning

confidence: 99%

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

2008

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We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH ∼ 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h ∼ M/320). We find that these highly spinning holes reach a maximum recoil velocity of ∼ 3300 km s −1 (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/mH ∼ 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of ∼ 4000 km s −1 and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highlyspinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(r −2 ) singularity at the puncture, rather than the usual O(r −4 ) singularity seen for non-maximal spins.

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Section: Discussionmentioning

confidence: 99%

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

2008

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“…We point out two directions to follow. The first is to consider 1 + log trumpet data sets for which the maximal sliced conditions is relaxed [20,26]. The second is to extend the present algorithm including more than one domain using the technique of domain decomposition.…”

Section: Final Remarksmentioning

confidence: 99%

“…The interest in constructing trumpet initial data has increased after the advent of the moving puncture method [4,5]. It has been shown that the Schwarzschild wormhole puncture data evolves in such a way the numerical slices tend a spatial slice with finite areal radius or trumpets [17][18][19][20]. Therefore, it is motivating to construct initial trumpet data for single and binary black holes endowed with spin and linear momentum.…”

Section: Introductionmentioning

confidence: 99%

Puncture black hole initial data: A single domain Galerkin-collocation method for trumpet and wormhole data sets

Clemente

Oliveira

2017

Phys. Rev. D

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We present a single domain Galerkin-Collocation method to calculate puncture initial data sets for single and binary, either in the trumpet or wormhole geometries. The combination of aspects belonging to the Galerkin and the Collocation methods together with the adoption of spherical coordinates in all cases show to be very effective. We have proposed a unified expression for the conformal factor to describe trumpet and spinning black holes. In particular, for the spinning trumpet black holes, we have exhibited the deformation of the limit surface due to the spin from a sphere to an oblate spheroid. We have also revisited the energy content in the trumpet and wormhole puncture data sets. The algorithm can be extended to describe binary black holes.

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“…As demonstrated by [8,9,10,11], dynamical simulations of a Schwarzschild spacetime using these coordinate conditions settle down to a spatial slice that terminates at a non-zero areal radius, and hence does not encounter the spacetime singularity at the center of the black hole. An embedding diagram of such a slice, which suggests the name trumpet data, is shown in Fig.…”

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confidence: 99%

“…An embedding diagram of such a slice, which suggests the name trumpet data, is shown in Fig. 2 of [11].Typically, moving-puncture simulations adopt initial data that are constructed using the puncture method [12,13,14]. As we explain in more detail below, the central idea of the puncture method is to write the conformal factor as a sum of an analytically known, singular background term, and a correction term that is unknown but regular.…”

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confidence: 99%

Trumpet-puncture initial data for black holes

Immerman

Baumgarte

2009

Phys. Rev. D

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We propose a new approach, based on the puncture method, to construct black hole initial data in the so-called trumpet geometry, i.e. on slices that asymptote to a limiting surface of non-zero areal radius. Our approach is easy to implement numerically and, at least for non-spinning black holes, does not require any internal boundary conditions. We present numerical results, obtained with a uniform-grid finite-difference code, for boosted black holes and binary black holes. We also comment on generalizations of this method for spinning black holes.PACS numbers: 04.20. Ex, 04.25.dg, 04.70.Bw Numerical simulations of black hole spacetimes have recently experienced a dramatic breakthrough (see [1,2,3] as well as numerous later publications). Most of these simulations now adopt some variation of the BSSN formulation [4,5] together with the moving puncture [2,3] method to handle the black hole singularities.The moving-puncture method is based on a set of empirically found coordinate conditions, namely the "1+log" slicing condition for the lapse [6] and a "Γ-freezing" gauge condition for the shift [7]. As demonstrated by [8,9,10,11], dynamical simulations of a Schwarzschild spacetime using these coordinate conditions settle down to a spatial slice that terminates at a non-zero areal radius, and hence does not encounter the spacetime singularity at the center of the black hole. An embedding diagram of such a slice, which suggests the name trumpet data, is shown in Fig. 2 of [11].Typically, moving-puncture simulations adopt initial data that are constructed using the puncture method [12,13,14]. As we explain in more detail below, the central idea of the puncture method is to write the conformal factor as a sum of an analytically known, singular background term, and a correction term that is unknown but regular. The equations for the correction term can then be solved everywhere, without any need for excision or any other means of dealing with the black hole singularity. To date, all applications of this method have adopted Schwarzschild data on a slice of constant Schwarzschild time as the background solution. These data connect spatial infinity in one universe with spatial infinity in another universe; the resulting initial data therefore represent wormhole data.Clearly, it would be desirable to produce initial data that represent black holes as trumpets rather than wormholes, since otherwise moving-puncture evolutions will drive the individual black holes to a trumpet geometry. Problems with one possible approach, based on a stationary 1+log slicing in the context of the conformal thin-sandwich decomposition, were described in [15]. Recently, trumpet initial data on hyperboloidal slices using * Also at Department of Physics, University of Illinois at UrbanaChampaign, Urbana, IL 61801 an excision method were constructed in [16]. In this paper we demonstrate how such data can be produced by generalizing the puncture method, which does not require any excision or internal boundary conditions, and is very easy to imple...

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

Cited by 121 publications

References 85 publications

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

Puncture black hole initial data: A single domain Galerkin-collocation method for trumpet and wormhole data sets

Trumpet-puncture initial data for black holes

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