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Title: Analytical representation of a black hole puncture solution

Abstract

The 'moving-puncture' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving-puncture simulations, the evolution of a single black hole leads to a well-known, time-independent, maximal slicing of Schwarzschild spacetime. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example, for testing and calibrating numerical codes that employ moving-puncture techniques. In this brief report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes.

Authors:
;  [1]
  1. Department of Physics and Astronomy, Bowdoin College, Brunswick, Maine 04011 (United States)
Publication Date:
OSTI Identifier:
21020219
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevD.75.067502; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; BLACK HOLES; COORDINATES; COSMOLOGY; MATHEMATICAL SOLUTIONS; NUMERICAL ANALYSIS; QUANTUM FIELD THEORY; SCHWARZSCHILD METRIC; SPACE-TIME

Citation Formats

Baumgarte, Thomas W., and Naculich, Stephen G. Analytical representation of a black hole puncture solution. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.067502.
Baumgarte, Thomas W., & Naculich, Stephen G. Analytical representation of a black hole puncture solution. United States. doi:10.1103/PHYSREVD.75.067502.
Baumgarte, Thomas W., and Naculich, Stephen G. Thu . "Analytical representation of a black hole puncture solution". United States. doi:10.1103/PHYSREVD.75.067502.
@article{osti_21020219,
title = {Analytical representation of a black hole puncture solution},
author = {Baumgarte, Thomas W. and Naculich, Stephen G.},
abstractNote = {The 'moving-puncture' technique has led to dramatic advancements in the numerical simulations of binary black holes. Hannam et al. have recently demonstrated that, for suitable gauge conditions commonly employed in moving-puncture simulations, the evolution of a single black hole leads to a well-known, time-independent, maximal slicing of Schwarzschild spacetime. They construct the corresponding solution in isotropic coordinates numerically and demonstrate its usefulness, for example, for testing and calibrating numerical codes that employ moving-puncture techniques. In this brief report we point out that this solution can also be constructed analytically, making it even more useful as a test case for numerical codes.},
doi = {10.1103/PHYSREVD.75.067502},
journal = {Physical Review. D, Particles Fields},
number = 6,
volume = 75,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • We solve for single distorted black hole initial data using the puncture method, where the Hamiltonian constraint is written as an elliptic equation in R{sup 3} for the nonsingular part of the metric conformal factor. With this approach we can generate isometric and nonisometric black hole data. For the isometric case, our data are directly comparable to those obtained by Bernstein et al., who impose isometry boundary conditions at the black hole throat. Our numerical simulations are performed using a parallel multigrid elliptic equation solver with adaptive mesh refinement. Mesh refinement allows us to use high resolution around the blackmore » hole while keeping the grid boundaries far away in the asymptotic region.« less
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  • We follow the inspiral and merger of equal-mass black holes (BHs) by the moving puncture technique and demonstrate that both the exterior solution and the asymptotic gravitational waveforms are unchanged when the initial interior solution is replaced by constraint-violating junk initial data. We apply this result to evolve conformal thin-sandwich (CTS) binary BH initial data by filling their excised interiors with arbitrary, but smooth, initial data and evolving with standard puncture gauge choices. The waveforms generated for both puncture and filled-CTS initial data are remarkably similar, and there are only minor differences between irrotational and corotational CTS BH binaries. Evenmore » the interior solutions appear to evolve to the same constraint-satisfying solution at late times, independent of the initial data.« less