Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes
arXiv:2409.17970 · doi:10.1088/1361-6382/ad9701
Abstract
In an attempt to simulate black hole echoes (generated by potential quantum-gravitational structure) in numerical relativity, we recently described how to implement a reflecting boundary outside of the horizon of a black hole in spherical symmetry. Here, we generalize this approach to spacetimes with no symmetries and implement it numerically using the generalized harmonic formulation. We cast the evolution equations and the numerical implementation into a Summation By Parts (SBP) scheme, which seats our method closer to a class of provably numerically stable systems. We implement an embedded boundary numerical framework that allows for arbitrarily shaped domains on a rectangular grid and even boundaries that evolve and move across the grid. As a demonstration of this framework, we study the evolution of gravitational wave scattering off a boundary either inside, or just outside, the horizon of a black hole. This marks a big leap toward the goal of a generic framework to obtain gravitational waveforms for behaviors motivated by quantum gravity near the horizons of merging black holes.
14 pages, 6 figures, final published version
References in corpus (23)
- Evolution of Binary Black Hole Spacetimes
- Numerical Relativity Using a Generalized Harmonic Decomposition
- Echoes from the Abyss: Tentative evidence for Planck-scale structure at black hole horizons
- A New Generalized Harmonic Evolution System
- Harmonic coordinate method for simulating generic singularities
- Well-Posed Initial-Boundary Evolution in General Relativity
- Gravitational wave echoes from black hole area quantization
- Testing outer boundary treatments for the Einstein equations
- Black hole evolution by spectral methods
- Echoes from Quantum Black Holes
- Boundary Conditions for the Einstein Evolution System
- Black-hole microstate spectroscopy: ringdown, quasinormal modes, and echoes
- Echoes from the Abyss: A highly spinning black hole remnant for the binary neutron star merger GW170817
- Black Hole Echology: The Observer's Manual
- On Reflectivity of Quantum Black Hole Horizons
- Hyperbolicity of second-order in space systems of evolution equations
- Effective Field Theory of Black Hole Echoes
- Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
- Fully relativistic three-dimensional Cauchy-characteristic matching for physical degrees of freedom
- Quasilocal Conservation Laws: Why We Need Them
- Efficient simulations of high-spin black holes with a new gauge
- Reflecting boundary conditions in numerical relativity as a model for black hole echoes
- Action Principle for the Generalized Harmonic Formulation of General Relativity