Gauge conditions for long-term numerical black hole evolutions without excision

By M. Alcubierre, B. Bruegmann, Peter Diener, M. Koppitz, D. Pollney, E. Seidel, Ryoji Takahashi. 2002

336 citations recorded by the source corpus.

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 gauge conditions we use is able to drive highly distorted, rotating black holes to an almost static state at late times, with well behaved metric functions, without the need for any special initial conditions or analytically prescribed gauge functions. Further, we show for the first time that one can extract accurate waveforms from these simulations, with the full machinery of excision or no excision and dynamic gauge conditions. The evolutions can be carried out for long times, far exceeding the longevity and accuracy of even better resolved 2D codes. While traditional 2D codes show errors in quantities such as apparent horizon mass of over 100% by t ≈ 100M, and crash by t ≈ 150M, with our new techniques the same systems can be evolved for more than hundreds of M’s in full 3D with errors of only a few percent.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/aefb6e42a93d96d7be8a22e215f57b01a8e86752

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

1. B. Kelly
2. J. Centrella
3. J. V. Meter
4. John G. Baker
5. Oliver DeWolfe
6. C. Rosen
7. D. Teaney
8. S. Gubser

In Nuclear and High Energy Physics

1. S. Gubser
2. Oliver DeWolfe
3. C. Rosen
4. D. Teaney
5. J. Centrella
6. J. V. Meter
7. B. Kelly
8. John G. Baker

Citations in the corpus

• Heavy ions and string theory (2013, methodology): “ of the current advances in numerical relativity using the BSSN formalism exploit the shift to select a numerically reasonable gauge based on the local derivatives of the induced metric, e.g. lm i lm [90,88,89]. Thus, in more rened BSSN treatment of boost invariant plasma, u would be non-zero and co”
• Numerical relativity using a generalized harmonic decomposition (2004, background): “The simplest class of gauge conditions that can be implement in this fashion are the so called “driver” conditions [45, 46, 47, 48, 49], where one directly specifies the time derivatives of α and β i to achieve, for example, approximate maximal slicing and minimal distortion gauges respectively.”
• Turduckening black holes: An Analytical and computational study (2008, methodology): “(5,6) is a generalization of the hyperbolic Gamma driver [15] condition where G(α, φ, x) and H(α, φ, x) are smooth, strictly positive functions, and η(B , α, x) is a smooth vector-valued function.”
• The Einstein Toolkit: a community computational infrastructure for relativistic astrophysics (2011, background): “The gauge functions f , K0, G, H, and η are determined by our choice of a 1 + log [151] slicing:”
• Gravitational Recoil from Spinning Binary Black Hole Mergers (2007, background): “In addition to the form of the evolution equations, the success of the MPR is due to the coordinate or gauge conditions (Alcubierre et al. 2003; Baker et al. 2006a; Campanelli et al. 2006a).”
• GRChombo: Numerical relativity with adaptive mesh refinement (2015, methodology): “We specify the evolution equation for i b using the gamma-driver conditions [35],”
• Unequal mass binary black hole plunges and gravitational recoil (2006, methodology): “The conformal factor φ is used to set the initial lapse as α = φ−2 [13, 21], while the initial shift is β = 0.”
• Black-hole binaries, gravitational waves, and numerical relativity (2010, background): “…2006; Rinne, 2010; van Meter et al., 2006b), but currently it is more common to impose artificial boundaries at finite spatial coordinates and apply some form of either radiative boundary condition (Alcubierre et al., 2003) or constraint-preserving boundary condition (Lindblom et al., 2006).”
• Black hole formation from axion stars (2016, methodology): “We use Sommerfeld boundary conditions [120], which allow outgoing waves to exit the grid with minimal reflections in the case of a φ2 potential.”