Harmonic coordinate method for simulating generic singularities
By David Garfinkle. 2001
151 citations recorded by the source corpus.
This paper presents both a numerical method for general relativity and an application of that method. The method involves the use of harmonic coordinates in a 3+1 code to evolve the Einstein equations with scalar field matter. In such coordinates, the terms in Einstein's equations with the highest number of derivatives take a form similar to that of the wave equation. The application is an exploration of the generic approach to the singularity for this type of matter. The preliminary results indicate that the dynamics as one approaches the singularity is locally the dynamics of the Kasner spacetimes.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/32da63be34f550c2767b1e89209bd957400b8407
How researchers see this paper
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In Astronomy and Astrophysics
- Benson Way
- Jorge E Santos
- J. V. Meter
- B. Kelly
- J. Centrella
- John G. Baker
- Ó. J. Dias
- Stuart L. Shapiro
In Nuclear and High Energy Physics
- Benson Way
- Jorge E Santos
- Ó. J. Dias
- J. Centrella
- J. V. Meter
- B. Kelly
- John G. Baker
- Frans Pretorius
Citations in the corpus
- Numerical relativity using a generalized harmonic decomposition (2004, methodology): “In numerical relativity, a solution scheme based directly upon this formulation of the field equations has recently been suggested by Garfinkle [20] (see also related work by Szilagyi and Winicour [21], and the so-called Z4 system [22], which seems to be quite similar to generalized harmonic evoluti”
- Numerical methods for finding stationary gravitational solutions (2015, background): “9) can be viewed as a global version of a local vector used to define generalised harmonic coordinates [531, 532].”
- Black-hole binaries, gravitational waves, and numerical relativity (2010, background): “…coordinate condition is too restrictive for numerical purposes, so generalized harmonic coordinates were eventually developed by introducing a source term into the coordinate condition, i.e. 2gx µ = Hµ (Friedrich, 1985; Garfinkle, 2002), a suitable choice for which preserves strong hyperbolicity.”
- Numerical relativity and compact binaries (2002, background): “…coordinate choice for the astrophysical situation at hand (but see Landry and Teukolsky (1999), where the traditional ADM approach together with harmonic coordinates and finely tuned finite differencing has been used to simulate the merger of binary neutron stars; see also Garfinkle (2002)).”