Numerical investigation of the late-time tails of the solutions of the Fackerell-Ipser equation
arXiv:2404.13447 · doi:10.1007/s10714-024-03316-7
Abstract
The late-time behaviour of the solutions of the Fackerell-Ipser equation (which is a wave equation for the spin-zero component of the electromagnetic field strength tensor) on the closure of the domain of outer communication of sub-extremal Kerr spacetime is studied numerically. Within the Kerr family, the case of Schwarzschild background is also considered. Horizon-penetrating compactified hyperboloidal coordinates are used, which allow the behaviour of the solutions to be observed at the event horizon and at future null infinity as well. For the initial data, pure multipole configurations that have compact support and are either stationary or non-stationary are taken. It is found that with such initial data the solutions of the Fackerell-Ipser equation converge at late times either to a known static solution (up to a constant factor) or to zero. As the limit is approached, the solutions exhibit a quasinormal ringdown and finally a power-law decay. The exponents characterizing the power-law decay of the spherical harmonic components of the field variable are extracted from the numerical data for various values of the parameters of the initial data, and based on the results a proposal for a Price's law relevant to the Fackerell-Ipser equation is made. Certain conserved energy and angular momentum currents are used to verify the numerical implementation of the underlying mathematical model. In the construction of these currents a discrete symmetry of the Fackerell-Ipser equation, which is the product of an equatorial reflection and a complex conjugation, is also taken into account.
29 pages, LaTeX, minor changes
References in corpus (82)
- Late-Time Behavior of Stellar Collapse and Explosions: I. Linearized Perturbations
- The linear stability of the Schwarzschild solution to gravitational perturbations
- Stability of Black Holes and Black Branes
- Hyperboloidal foliations and scri-fixing
- Dynamics of perturbations of rotating black holes
- Quasinormal modes of nearly extremal Kerr spacetimes: spectrum bifurcation and power-law ringdown
- Decay of Solutions of the Wave Equation in the Kerr Geometry
- Late-time dynamics of rapidly rotating black holes
- Late-time decay of scalar perturbations outside rotating black holes
- A proof of Price's Law on Schwarzschild black hole manifolds for all angular momenta
- Dynamics of Scalar Fields in the Background of Rotating Black Holes
- Information, Relative Entropy of Entanglement and Irreversibility
- Radiative Tail of Realistic Rotating Gravitational Collapse
- Numerical computation of second order vacuum perturbations of Kerr black holes
- Quantitative Mode Stability for the Wave Equation on the Kerr Spacetime
- Late time dynamics of scalar perturbations outside black holes: II. Schwarzschild geometry
- Mode-Coupling in Rotating Gravitational Collapse of a Scalar Field
- Numerical solution of the 2+1 Teukolsky equation on a hyperboloidal and horizon penetrating foliation of Kerr and application to late-time decays
- Numerical integration of the Teukolsky Equation in the time domain
- Hyperboloidal slicing approach to quasi-normal mode expansions: the Reissner-Nordström case
- Horizon Instability of Extremal Kerr Black Holes: Nonaxisymmetric Modes and Enhanced Growth Rate
- Numerical investigation of the late-time Kerr tails
- Hyperboloidal framework for the Kerr spacetime
- A superradiance resonance cavity outside rapidly rotating black holes
- Late time tails in the Kerr spacetime
- Late time decay of scalar, electromagnetic, and gravitational perturbations outside rotating black holes
- Spacelike matching to null infinity
- 3D simulations of linearized scalar fields in Kerr spacetime
- Mode-coupling in rotating gravitational collapse: Gravitational and electromagnetic perturbations
- What does a strongly excited 't Hooft-Polyakov magnetic monopole do?
- Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
- Conserved currents for Kerr and orthogonality of quasinormal modes
- High accuracy simulations of Kerr tails: coordinate dependence and higher multipoles
- Teukolsky Master Equation: De Rham wave equation for the gravitational and electromagnetic fields in vacuum
- Axisymmetric fully spectral code for hyperbolic equations
- Linearized gravity and gauge conditions
- Intermediate behavior of Kerr tails
- Radiative falloff of a scalar field in a weakly curved spacetime without symmetries
- Late time tails from momentarily stationary, compact initial data in Schwarzschild spacetimes
- Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole II: linearized gravity
- Mode coupling mechanism for late-time Kerr tails
- Late-time decay of gravitational and electromagnetic perturbations along the event horizon
- Mode stability for the Teukolsky equation on extremal and subextremal Kerr spacetimes
- Late-time Kerr tails revisited
- High-order Tail in Schwarzschild Space-time
- Pointwise decay for the Maxwell field on black hole space-times
- Critical Exponents of Extremal Kerr Perturbations
- The linear stability of Reissner-Nordström spacetime: the full subextremal range
- Late-Time Dynamics of Scalar Fields on Rotating Black Hole Backgrounds
- Asymptotically null slices in numerical relativity: mathematical analysis and spherical wave equation tests
- Numerical investigation of highly excited magnetic monopoles in SU(2) Yang-Mills-Higgs theory
- Non-modal linear stability of the Schwarzschild black hole
- Linear Stability of the Non-Extreme Kerr Black Hole
- Hyperboloidal evolution of test fields in three spatial dimensions
- Decay of solutions to the Maxwell equation on the Schwarzschild background
- On the Use of Multipole Expansion in Time Evolution of Non-linear Dynamical Systems and Some Surprises Related to Superradiance
- Late-time Kerr tails: generic and non-generic initial data sets, "up" modes, and superposition
- Dynamical excitation of space-time modes of compact objects
- On the Relation Between Asymptotic Charges, the Failure of Peeling and Late-time Tails
- The linear stability of Reissner-Nordström spacetime for small charge
- Uniform energy bound and Morawetz estimate for extreme components of spin fields in the exterior of a slowly rotating Kerr black hole I: Maxwell field
- Linearized Stability of Extreme Black Holes
- High-order tail in Kerr spacetime
- Price's law and precise late-time asymptotics for subextremal Reissner-Nordström black holes
- Numerical investigation of the dynamics of linear spin fields on Kerr background I. Late time tails of spin fields
- Spin geometry and conservation laws in the Kerr spacetime
- Scalar Fields in Black Hole Spacetimes
- Symmetry operators and decoupled equations for linear fields on black hole spacetimes
- Perturbations of Extremal Kerr Spacetime: Analytic Framework and Late-time Tails
- Comments on tails in Schwarzschild spacetimes
- A geometric description of Maxwell field in a Kerr spacetime
- On the linear stability of the extreme Kerr black hole under axially symmetric perturbations
- Hyperboloidal slices for the wave equation of Kerr-Schild metrics and numerical applications
- Price's law for spin fields on a Schwarzschild background
- Noether currents for the Teukolsky Master Equation
- A class of conserved currents for linearized gravity in the Kerr spacetime
- Conserved currents for electromagnetic fields in the Kerr spacetime
- A note on boundary value problems for black hole evolutions
- A Conserved Energy for Axially Symmetric Newman-Penrose-Maxwell Scalars on Kerr Black Holes
- Numerical investigation of the dynamics of linear spin fields on a Kerr background II: Superradiant scattering
- Stability of stationary-axisymmetric black holes in vacuum general relativity to axisymmetric electromagnetic perturbations
- Bounds for axially symmetric linear perturbations for the extreme Kerr black hole