Local Continuity of Angular Momentum and Noether Charge for Matter in General Relativity
arXiv:2203.13845 · doi:10.1088/1361-6382/accc6a
Abstract
Conservation laws have many applications in numerical relativity. However, it is not straightforward to define local conservation laws for general dynamic spacetimes due the lack of coordinate translation symmetries. In flat space, the rate of change of energy-momentum within a finite spacelike volume is equivalent to the flux integrated over the surface of this volume; for general spacetimes it is necessary to include a volume integral of a source term arising from spacetime curvature. In this work a study of continuity of matter in general relativity is extended to include angular momentum of matter and Noether currents associated with gauge symmetries. Expressions for the Noether charge and flux of complex scalar fields and complex Proca fields are found using this formalism. Expressions for the angular momentum density, flux and source are also derived which are then applied to a numerical relativity collision of boson stars in 3D with non-zero impact parameter as an illustration of the methods.
arXiv comment14 pages, 9 figures
References in corpus (17)
- The Dynamics of General Relativity
- Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Gauge conditions for long-term numerical black hole evolutions without excision
- Conformal and covariant formulation of the Z4 system with constraint-violation damping
- 3+1 Formalism and Bases of Numerical Relativity
- General-covariant evolution formalism for Numerical Relativity
- GRChombo : Numerical Relativity with Adaptive Mesh Refinement
- Superradiant instability of massive vector fields around spinning black holes in the relativistic regime
- GRChombo: An adaptable numerical relativity code for fundamental physics
- Nonlinear interactions between black holes and Proca fields
- Head-on collisions and orbital mergers of Proca stars
- On the dynamical bar-mode instability in spinning bosonic stars
- Vector boson star solutions with a quartic order self-interaction
- Malaise and remedy of binary boson-star initial data
- Growth of accretion driven scalar hair around Kerr black holes
- Continuity equations for general matter: applications in numerical relativity