On the Linear Regime of the Characteristic formulation of General relativity in the Minkowski and Schwarzschild's Backgrounds
arXiv:1611.05614
Abstract
We present here the linear regime of the Einstein's field equations in the characteristic formulation. Through a simple decomposition of the metric variables in spin-weighted spherical harmonics, the field equations are expressed as a system of coupled ordinary differential equations. The process for decoupling them leads to a simple equation for - one of the Bondi-Sachs metric variables - known in the literature as the master equation. Then, this last equation is solved in terms of Bessel's functions of the first kind for the Minkowski's background, and in terms of the Heun's function in the Schwarzschild's case. In addition, when a matter source is considered, the boundary conditions across the time-like world tubes bounding the source are taken into account. These boundary conditions are computed for all multipole modes. Some examples as the point particle binaries in circular and eccentric orbits, in the Minkowski's background are shown as particular cases of this formalism.
arXiv comment132 pages, 17 figures
References in corpus (30)
- Numerical Relativity: A review
- Dynamical mass ejection from black hole-neutron star binaries
- Gravitational and electromagnetic outputs from binary neutron star mergers
- High-powered Gravitational News
- Numerical Relativity and Astrophysics
- Numerical Relativity in Spherical Polar Coordinates: Evolution Calculations with the BSSN Formulation
- Gravitational Wave Extraction in Simulations of Rotating Stellar Core Collapse
- Mode coupling in the nonlinear response of black holes
- The Dynamical Evolution of Black Hole-Neutron Star Binaries in General Relativity: Simulations of Tidal Disruption
- A Characteristic Extraction Tool for Gravitational Waveforms
- Modeling the remnant mass, spin, and recoil from unequal-mass, precessing black-hole binaries: The Intermediate Mass Ratio Regime
- Linking electromagnetic and gravitational radiation in coalescing binary neutron stars
- Strategies for the Characteristic Extraction of Gravitational Waveforms
- Linearized solutions of the Einstein equations within a Bondi-Sachs framework, and implications for boundary conditions in numerical simulations
- Numerical relativity with characteristic evolution, using six angular patches
- Gravitational waves in a de Sitter universe
- Gravitational waveforms with controlled accuracy
- On characteristic initial data for a star orbiting a black hole
- General relativistic null-cone evolutions with a high-order scheme
- Initial data transients in binary black hole evolutions
- First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
- Well-posed first-order reduction of the characteristic problem of the linearized Einstein equations
- Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method
- Numerical evolution of radiative Robinson-Trautman spacetimes
- Extended two-dimensional characteristic framework to study nonrotating black holes
- Global energy conservation in nonlinear spherical characteristic evolutions
- Gravitational Waves, Sources, and Detectors
- Point Particle Binary System with Components of Different Masses in the Linear Regime of the Characteristic Formulation of General Relativity
- Gravitational Waves I: Basic Emission Equations
- Gravitational radiation by point particle eccentric binary systems in the linearised characteristic formulation of general relativity