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Evolution of Distorted Black Holes: A Perturbative Approach
General Relativity and Quantum Cosmology · Submitted 3 Jun 1998
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim In addition to exploring the physics of these distorted black hole data sets, in particular allowing an exploration of linear, nonlinear, and mode mixing effects, this approach provides an important testbed for any fully nonlinear numerical code designed to evolve black hole spacetimes in 2D or 3D.
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The abstract, sentence by sentence
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and 3D distorted black hole spacetimes. In 2D, waveforms for different modes of the radiation are presented, comparing full nonlinear evolutions for different axisymmetric l-modes with perturbative evolutions. We show how axisymmetric black hole codes solving the full, nonlinear Einstein equations are capable of very accurate evolutions, and also how these techniques aid in studying nonlinear effects. In 3D we show how the initial data for the perturbation equations can be computed, and we compare with analytic solutions given from a perturbative expansion of the initial value problem. In addition to exploring the physics of these distorted black hole data sets, in particular allowing an exploration of linear, nonlinear, and mode mixing effects, this approach provides an important testbed for any fully nonlinear numerical code designed to evolve black hole spacetimes in 2D or 3D.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. | contribution 0.56 | 0.94 | 0.06 | asserted 0.97 |
| s1 | We apply this to 2D and 3D distorted black hole spacetimes. | contribution 0.61 | 0.90 | 0.03 | asserted 0.96 |
| s2 | In 2D, waveforms for different modes of the radiation are presented, comparing full nonlinear evolutions for different axisymmetric l-modes with perturbative evolutions. | result 0.64 | 0.92 | 0.08 | asserted 0.97 |
| s3 | We show how axisymmetric black hole codes solving the full, nonlinear Einstein equations are capable of very accurate evolutions, and also how these techniques aid in studying nonlinear effects. | interpretation 0.50 | 0.76 | 0.21 | asserted 1.00 |
| s4 | In 3D we show how the initial data for the perturbation equations can be computed, and we compare with analytic solutions given from a perturbative expansion of the initial value problem. | method 0.54 | 0.92 | 0.07 | asserted 1.00 |
| s5 | In addition to exploring the physics of these distorted black hole data sets, in particular allowing an exploration of linear, nonlinear, and mode mixing effects, this approach provides an important testbed for any fully nonlinear numerical code designed to evolve black hole spacetimes in 2D or 3D. | interpretation 0.83 | 0.58 | 0.52 | asserted 0.94 |
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Original abstract
We consider a series of distorted black hole initial data sets, and develop techniques to evolve them using the linearized equations of motion for the gravitational wave perturbations on a Schwarzschild background. We apply this to 2D and 3D distorted black hole spacetimes. In 2D, waveforms for different modes of the radiation are presented, comparing full nonlinear evolutions for different axisymmetric l-modes with perturbative evolutions. We show how axisymmetric black hole codes solving the full, nonlinear Einstein equations are capable of very accurate evolutions, and also how these techniques aid in studying nonlinear effects. In 3D we show how the initial data for the perturbation equations can be computed, and we compare with analytic solutions given from a perturbative expansion of the initial value problem. In addition to exploring the physics of these distorted black hole data sets, in particular allowing an exploration of linear, nonlinear, and mode mixing effects, this approach provides an important testbed for any fully nonlinear numerical code designed to evolve black hole spacetimes in 2D or 3D.
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To distinguish linear and nonlinear contributions, we adopt a close-limit type framework [ref] , in which we evolve a single perturbed black hole by numerically integrating both the linearized and nonlinear Einstein equations.
Imprints of Changing Mass and Spin on Black Hole Ringdown · Introduction · 0.99
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