A minimal no-radiation approximation to Einstein's field equations
arXiv:gr-qc/0310041 · doi:10.1103/PhysRevD.69.021501
Abstract
An approximation to Einstein's field equations in Arnowitt-Deser-Misner (ADM) canonical formalism is presented which corresponds to the magneto-hydrodynamics (MHD) approximation in electrodynamics. It results in coupled elliptic equations which represent the maximum of elliptic-type structure of Einstein's theory and naturally generalizes previous conformal-flat truncations of the theory. The Hamiltonian, in this approximation, is identical with the non-dissipative part of the Einsteinian one through the third post-Newtonian order. The proposed scheme, where stationary spacetimes are exactly reproduced, should be useful to construct {\em realistic} initial data for general relativistic simulations as well as to model astrophysical scenarios, where gravitational radiation reaction can be neglected.
9 pages
References in corpus (2)
Cited by in corpus (13)
- Binary Neutron Star Mergers
- A 3+1 perspective on null hypersurfaces and isolated horizons
- Excision boundary conditions for black hole initial data
- Why do naked singularities form in gravitational collapse?
- Gravitational Recoil during Binary Black Hole Coalescence using the Effective One Body Approach
- "Mariage des Maillages": A new numerical approach for 3D relativistic core collapse simulations
- Deriving formulations for numerical computation of binary neutron stars in quasicircular orbits
- Binary neutron stars: Equilibrium models beyond spatial conformal flatness
- Non-conformally flat initial data for binary compact objects
- On the existence of initial data containing isolated black holes
- Numerical implementation of isolated horizon boundary conditions
- A Numerical Study of Boson Star Binaries
- Fourth-post-Newtonian-exact approximation to General Relativity