Conformally flat slices of asymptotically flat spacetimes
arXiv:1909.06135 · doi:10.1088/1361-6382/ab852b
Abstract
For mathematical convenience initial data sets in numerical relativity are often taken to be conformally flat. Employing the dual-foliation formalism, we investigate the physical consequences of this assumption. Working within a large class of asymptotically flat spacetimes we show that the ADM linear momentum is governed by the leading Lorentz part of a boost even in the presence of supertranslation-like terms. Following up, we find that in spacetimes that are asymptotically flat, and admit spatial slices with vanishing linear momentum that are sufficiently close to conformal flatness, any boosted slice can not be conformally flat. Consequently there are no conformally flat boosted slices of the Schwarzschild spacetime. This confirms the previously anticipated explanation for the presence of junk-radiation in Brandt-Bruegmann puncture data.
arXiv comment11 pages, 1 figure
References in corpus (20)
- A simple construction of initial data for multiple black holes
- Conformal ``thin sandwich'' data for the initial-value problem of general relativity
- Extrinsic Curvature and the Einstein Constraints
- The high-energy collision of two black holes
- Cross section, final spin and zoom-whirl behavior in high-energy black hole collisions
- High-velocity collision of two black holes
- Waveless Approximation Theories of Gravity
- General Relativistic Models of Binary Neutron Stars in Quasiequilibrium
- A new numerical method for constructing quasi-equilibrium sequences of irrotational binary neutron stars in general relativity
- On the nonexistence of conformally flat slices in the Kerr and other stationary spacetimes
- Asymptotic expansions of the Cotton-York tensor on slices of stationary spacetimes
- High Energy Collisions of Black Holes Numerically Revisited
- Gauge invariant formalism for second order perturbations of Schwarzschild spacetimes
- Puncture Initial Data for Black-Hole Binaries with High Spins and High Boosts
- Constraints as evolutionary systems
- Revisiting Hyperbolicity of Relativistic Fluids
- The Weak Null Condition in Free-evolution Schemes for Numerical Relativity: Dual Foliation GHG with Constraint Damping
- Hyperbolicity of Physical Theories with Application to General Relativity
- Hyperbolicity of Divergence Cleaning and Vector Potential Formulations of GRMHD
- Coping with Junk Radiation in Binary Black Hole Simulations