Three-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity

Barreto, W.; Silva, A. Da; Gómez, Roberto; Lehner, Luis; Rosales, Luis; Winicour, Jeffrey

doi:10.1103/physrevd.71.064028

Cited by 17 publications

(22 citation statements)

References 53 publications

(80 reference statements)

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“…For Kerr black holes as well as for other astrophysical or string theory motivated cases, quasinormal modes form a countable set of discrete frequencies 4. Quasinormal modes calculated in the linear approximation are in good agreement with those obtained by the fully nonlinear integration of the Einstein equations, at least at sufficiently late time 31,32 .…”

Section: Methods For Quasinormal Modes Calculationssupporting

confidence: 76%

Quasinormal modes of black holes: From astrophysics to string theory

2011

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Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past ten years in string theory, brane-world models and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes (QNMs), allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, AdS/CFT interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

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Section: Methods For Quasinormal Modes Calculationssupporting

confidence: 76%

Quasinormal modes of black holes: From astrophysics to string theory

2011

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“…II, because of the fixed overlap between patches, a significant portion of the grid is wasted. While this might be acceptable in small scale simulations [6,9,10,11], it needs to be addressed in the context of large scale computations as in that case it translates into a serious waste of computational resources.…”

Section: A Parallelization Of Existing Characteristic Codesmentioning

confidence: 99%

“…[8] for a description of the vacuum problem, and Ref. [11] for the coupling of the scalar field to the gravitational metric fields. We use coordinates based upon a family of outgoing null hypersurfaces, and we let u label these hypersurfaces, x A (A = 2, 3) label the null rays and r be a surface area coordinate.…”

Section: A Three-dimensional Massless Scalar Field Scattered Off Amentioning

confidence: 99%

“…Treating the Einstein-Klein-Gordon model problem consistently within the LEO framework requires some modifications to [11], specifically to the wave equation for the scalar field ( φ = 0) which is given by Eqs. (21)- (27) of [11].…”

Section: A Three-dimensional Massless Scalar Field Scattered Off Amentioning

confidence: 99%

“…A significant computational effort is nevertheless necessary to extend its range of applicability to the simulation of astrophysically relevant sources of gravitational radiation, such as the black hole -neutron star binary problem, where the approach can be most useful. As work on the characteristic formulation to date illustrates [6,9,10,11], it is clear that most three-dimensional characteristic simulations, even vacuum simulations [9] are resolution-limited. This is particularly true of three-dimensional simulations of systems containing compact matter sources [10], even when the matter source is an extended one.…”

Section: Introductionmentioning

confidence: 99%

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Framework for large-scale relativistic simulations in the characteristic approach

2007

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We present a new computational framework (LEO), that enables us to carry out the very first large-scale, high-resolution computations in the context of the characteristic approach in numerical relativity. At the analytic level, our approach is based on a new implementation of the "eth" formalism, using a non-standard representation of the spin-raising and lowering angular operators in terms of non-conformal coordinates on the sphere; we couple this formalism to a partially firstorder reduction (in the angular variables) of the Einstein equations. The numerical implementation of our approach supplies the basic building blocks for a highly parallel, easily extensible numerical code. We demonstrate the adaptability and excellent scaling of our numerical code by solving, within our numerical framework, for a scalar field minimally coupled to gravity (the Einstein-KleinGordon problem) in the 3-dimensions. The nonlinear code is globally second-order convergent, and has been extensively tested using as reference a calibrated code with the same boundary-initial data and radial marching algorithm. In this context, we show how accurately we can follow quasi-normal mode ringing. In the linear regime, we show energy conservation for a number of initial data sets with varying angular structure. A striking result that arises in this context is the saturation of the flow of energy through the Schwarzschild radius. As a final calibration check we perform a large simulation with resolution never achieved before.

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