Why Solve the Hamiltonian Constraint in Numerical Relativity?
Beverly K. Berger
Abstract
The indefinite sign of the Hamiltonian constraint means that solutions to Einstein's equations must achieve a delicate balance--often among numerically large terms that nearly cancel. If numerical errors cause a violation of the Hamiltonian constraint, the failure of the delicate balance could lead to qualitatively wrong behavior rather than just decreased accuracy. This issue is different from instabilities caused by constraint-violating modes. Examples of stable numerical simulations of collapsing cosmological spacetimes exhibiting local mixmaster dynamics with and without Hamiltonian constraint enforcement are presented.
Create a lesson
Related papers
Multimessenger astrophysics drives the case for an Australian Gravitational-Wave observatory
Fiona H. Panther, Paul D. Lasky, Nikhil Sarin
Binary black hole mergers in massive Einstein-scalar-Gauss-Bonnet gravity
Harry L. H. Shum, Llibert Aresté Saló, Miguel Bezares et al.
Noisy pipelines II: Non-parametric Noise Inference for LISA
Charlie Hoy, Joseph Bayley, Ollie Burke et al.
Quasi-Normal Modes of Covariant Loop Quantum Black Holes
Chao Zhang, Sushant G. Ghosh, Anzhong Wang
Kerr metric perturbations for second-order self-force theory
Benjamin Leather, Samuel D. Upton, Patrick Bourg et al.
Multi-domain spectral method for Kerr spacetimes: a hyperboloidal Teukolsky m-mode solver for self-force computations
Brad Cownden, Rodrigo Panosso Macedo, Christiana Pantelidou et al.