Spectral approach to axisymmetric evolution of Einstein's equations
arXiv:1410.2548 · doi:10.1088/1742-6596/600/1/012060
Abstract
We present a new formulation of Einstein's equations for an axisymmetric spacetime with vanishing twist in vacuum. We propose a fully constrained scheme and use spherical polar coordinates. A general problem for this choice is the occurrence of coordinate singularities on the axis of symmetry and at the origin. Spherical harmonics are manifestly regular on the axis and hence take care of that issue automatically. In addition a spectral approach has computational advantages when the equations are implemented. Therefore we spectrally decompose all the variables in the appropriate harmonics. A central point in the formulation is the gauge choice. One of our results is that the commonly used maximal-isothermal gauge turns out to be incompatible with tensor harmonic expansions, and we introduce a new gauge that is better suited. We also address the regularisation of the coordinate singularity at the origin.
arXiv comment6 pages, based on a talk given by one of the authors at the Spanish Relativity Meeting ERE14 in Valencia, published version
References in corpus (11)
- A constrained scheme for Einstein equations based on Dirac gauge and spherical coordinates
- Key Elements of Robustness in Binary Black Hole Evolutions using Spectral Methods
- An Axisymmetric Gravitational Collapse Code
- Numerical evolution of Brill waves
- Symmetries of asymptotically flat electrovacuum spacetimes and radiation
- Constrained evolution in axisymmetry and the gravitational collapse of prolate Brill waves
- On critical collapse of gravitational waves
- On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance
- Explicit solution of the linearized Einstein equations in TT gauge for all multipoles
- Summation by parts methods for the spherical harmonic decomposition of the wave equation in arbitrary dimensions
- Axially symmetric spacetimes: numerical and analytical perspectives