Numerical investigation of the dynamics of linear spin s fields on a Kerr background: Late-time tails of spin s=±1,±2 fields numerical investigation of the dynamics of linear ... Csukás, Rácz, and Tóth

Károly Csukás, István Rácz, Gábor Zsolt Tóth

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Abstract

The time evolution of linear fields of spin s=±1 and s=±2 on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics, which allows us to evaluate all angular derivatives analytically, whereas the evolution of the expansion coefficients in the time-radial section is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations, single mode excitations-either static or purely dynamical-type initial data- A re applied. Within this setup the late-time tail behavior is investigated. Because of the applied conformal compactification, the asymptotic decay rates are determined at three characteristic locations-in the domain of outer communication, at the event horizon, and at future null infinity-simultaneously. A recently introduced new type of "energy" and "angular momentum" balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema and also to verify the proper implementation of the underlying mathematical model.

Original languageEnglish
Article number104025
JournalPhysical Review D
Volume100
Issue number10
DOIs
Publication statusPublished - Nov 18 2019

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event horizon
spherical harmonics
boundary value problems
infinity
decay rates
mathematical models
angular momentum
communication
expansion
coefficients
excitation
energy

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

Cite this

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title = "Numerical investigation of the dynamics of linear spin s fields on a Kerr background: Late-time tails of spin s=±1,±2 fields numerical investigation of the dynamics of linear ... Csuk{\'a}s, R{\'a}cz, and T{\'o}th",
abstract = "The time evolution of linear fields of spin s=±1 and s=±2 on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of conformal compactification and the hyperbolic initial value problem. The evolved basic variables are expanded in terms of spin-weighted spherical harmonics, which allows us to evaluate all angular derivatives analytically, whereas the evolution of the expansion coefficients in the time-radial section is determined by applying the method of lines implemented in a fourth order accurate finite differencing stencil. Concerning the initialization, in all of our investigations, single mode excitations-either static or purely dynamical-type initial data- A re applied. Within this setup the late-time tail behavior is investigated. Because of the applied conformal compactification, the asymptotic decay rates are determined at three characteristic locations-in the domain of outer communication, at the event horizon, and at future null infinity-simultaneously. A recently introduced new type of {"}energy{"} and {"}angular momentum{"} balance relations are also applied in order to demonstrate the feasibility and robustness of the developed numerical schema and also to verify the proper implementation of the underlying mathematical model.",
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