Dynamics of scalar fields in the background of rotating black holes

Krivan, William; Laguna, Pablo; Papadopoulos, Philippos

doi:10.1103/physrevd.54.4728

Cited by 81 publications

(135 citation statements)

References 10 publications

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“…(25), in the rest of this section we analyze evolutions of different initial data sets, all of them consisting of a combination of (ℓ = 2, m = 2) and (ℓ = 2, m = −2) modes with A = 0 and B = 1. We numerically explore the dependence of the amplitudes of the counter-and co-rotating fundamental modes (in the next subsection we will study overtones) on the width σ of the initial data [cf.…”

Section: E Relative Amplitude Of Corotating and Counterrotating Modesmentioning

confidence: 99%

Numerical study of the quasinormal mode excitation of Kerr black holes

Dorband

Berti²,

Diener

et al. 2006

Phys. Rev. D

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We present numerical results from three-dimensional evolutions of scalar perturbations of Kerr black holes. Our simulations make use of a high-order accurate multi-block code which naturally allows for fixed adaptivity and smooth inner (excision) and outer boundaries. We focus on the quasinormal ringing phase, presenting a systematic method for extraction of the quasinormal mode frequencies and amplitudes and comparing our results against perturbation theory.The detection of a single mode in a ringdown waveform allows for a measurement of the mass and spin of a black hole; a multimode detection would allow a test of the Kerr nature of the source. Since the possibility of a multimode detection depends on the relative mode amplitude, we study this topic in some detail. The amplitude of each mode depends exponentially on the starting time of the quasinormal regime, which is not defined unambiguously. We show that this time-shift problem can be circumvented by looking at appropriately chosen relative mode amplitudes. From our simulations we extract the quasinormal frequencies and the relative and absolute amplitudes of corotating and counterrotating modes (including overtones in the corotating case). We study the dependence of these amplitudes on the shape of the initial perturbation, the angular dependence of the mode and the black hole spin, comparing against results from perturbation theory in the so-called asymptotic approximation. We also compare the quasinormal frequencies from our numerical simulations with predictions from perturbation theory, finding excellent agreement. For rapidly rotating black holes (of spin j = 0.98) we can extract the quasinormal frequencies of not only the fundamental mode, but also of the first two overtones. Finally we study under what conditions the relative amplitude between given pairs of modes gets maximally excited and present a quantitative analysis of rotational mode-mode coupling. The main conclusions and techniques of our analysis are quite general and, as such, should be of interest in the study of ringdown gravitational waves produced by astrophysical gravitational wave sources.

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Section: E Relative Amplitude Of Corotating and Counterrotating Modesmentioning

confidence: 99%

Numerical study of the quasinormal mode excitation of Kerr black holes

Dorband

Berti²,

Diener

et al. 2006

Phys. Rev. D

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“…This topic has been the subject of both analytical [33][34][35][36][37][38] and numerical [39][40][41] investigation. For the purpose of this discussion we rely mostly on the analytical description of the late-time behavior of a scalar field provided by Hod [37].…”

Section: Radiative Falloff In Kerrmentioning

confidence: 99%

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

Poisson

2002

Phys. Rev. D

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We consider a massless scalar field propagating in a weakly curved spacetime whose metric is a solution to the linearized Einstein field equations. The spacetime is assumed to be stationary and asymptotically flat, but no other symmetries are imposed -the spacetime can rotate and deviate strongly from spherical symmetry. We prove that the late-time behavior of the scalar field is identical to what it would be in a spherically-symmetric spacetime: it decays in time according to an inverse power-law, with a power determined by the angular profile of the initial wave packet (Price falloff theorem). The field's late-time dynamics is insensitive to the nonspherical aspects of the metric, and it is governed entirely by the spacetime's total gravitational mass; other multipole moments, and in particular the spacetime's total angular momentum, do not enter in the description of the field's late-time behavior. This extended formulation of Price's falloff theorem appears to be at odds with previous studies of radiative decay in the spacetime of a Kerr black hole. We show, however, that the contradiction is only apparent, and that it is largely an artifact of the Boyer-Lindquist coordinates adopted in these studies.

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“…Over the past decade, several authors have considered evolution in 2+1D, with or without a particle source. Krivan et al [24,25] explored the late-time decay of scalar fields and Weyl-scalar vacuum perturbations by evolving the master Teukolsky equation in 2+1D. Pazos-Avalos and Lousto [26] presented an improved, fourth-order-convergent code in 2+1D, for the evolution of vacuum perturbations of the Teukolsky equation.…”

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confidence: 99%

m-mode regularization scheme for the self-force in Kerr spacetime

2007

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We present a new, simple method for calculating the scalar, electromagnetic, and gravitational self forces acting on particles in orbit around a Kerr black hole. The standard "mode-sum regularization" approach for self-force calculations relies on a decomposition of the full (retarded) perturbation field into multipole modes, followed by the application of a certain mode-by-mode regularization procedure. In recent years several groups have developed numerical codes for calculating black hole perturbations directly in 2+1 dimensions (i.e., decomposing the azimuthal dependence into mmodes, but refraining from a full multipole decomposition). Here we formulate a practical scheme for constructing the self force directly from the 2+1-dimensional m-modes. While the standard mode-sum method is serving well in calculations of the self force in Schwarzschild geometry, the new scheme should allow a more efficient treatment of the Kerr problem.

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Dynamics of scalar fields in the background of rotating black holes

Cited by 81 publications

References 10 publications

Numerical study of the quasinormal mode excitation of Kerr black holes

Numerical study of the quasinormal mode excitation of Kerr black holes

Radiative falloff of a scalar field in a weakly curved spacetime without symmetries

m-mode regularization scheme for the self-force in Kerr spacetime

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