Numerical relativity using a generalized harmonic decomposition
By Frans Pretorius. 2004
311 citations recorded by the source corpus.
A new numerical scheme to solve the Einstein field equations based upon the generalized harmonic decomposition of the Ricci tensor is introduced. The source functions driving the wave equations that define generalized harmonic coordinates are treated as independent functions, and encode the coordinate freedom of solutions. Techniques are discussed to impose particular gauge conditions through a specification of the source functions. A 3D, free evolution, finite difference code implementing this system of equations with a scalar field matter source is described. The second-order-in-space-and-time partial differential equations are discretized directly without the use of first-order auxiliary terms, limiting the number of independent functions to 15—ten metric quantities, four source functions and the scalar field. This also limits the number of constraint equations, which can only be enforced to within truncation error in a numerical free evolution, to four. The coordinate system is compactified to spatial infinity in order to impose physically motivated, constraint-preserving outer boundary conditions. A variant of the cartoon method for efficiently simulating axisymmetric spacetimes with a Cartesian code is described that does not use interpolation, and is easier to incorporate into existing adaptive mesh refinement packages. Preliminary test simulations of vacuum black-hole evolution and black-hole formation via scalar field collapse are described, suggesting that this method may be useful for studying many spacetimes of interest.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/52bfc583d6cf17c5c9e4e5585c68130216f75d60
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Citations in the corpus
- Numerical methods for finding stationary gravitational solutions (2015, background): “These include the characteristic formalism [2, 3], the ADM, BSSN, Z4 formalisms [4–10], and the generalized harmonic gauge formulation [11–16].”
- Black-hole binaries, gravitational waves, and numerical relativity (2010, methodology): “Pretorius had clearly developed a robust method for evolving black-hole binary mergers.”
- Future stability of the Einstein-non-linear scalar field system (2008, background): “However, there is one significant difference; in the present paper, as well as in [22], the gauge source functions are given explicitly in terms of the metric whereas in [25], the gauge source functions obey certain equations, so that one obtains a coupled system for the metric components, the scala”
- Reducing orbital eccentricity in binary black hole simulations (2007, background): “This code evolves a first-order representation [32] of the generalized harmonic system [33, 34].”
- Beginning inflation in an inhomogeneous universe (2015, methodology): “equations in the generalized harmonic formulation using the code described in [23, 24].”
- A new generalized harmonic evolution system (2005, methodology): “So, this system has constraint suppression properties that are similar to those of the Pretorius (and Gundlach, et al.) system.”
- Heavy ions and string theory (2013, methodology): “As explained in [19], most of the thermodynamic observables are easily computed using the method of scalar variables, [19, 76].”