Extended two-dimensional characteristic framework to study nonrotating black holes

Abstract

We develop a numerical solver, that extends the computational framework considered in [Phys. Rev. D 65, 084016 (2002)], to include scalar perturbations of nonrotating black holes. The nonlinear Einstein-Klein-Gordon equations for a massless scalar field minimally coupled to gravity are solved in two spatial dimensions (2D). The numerical procedure is based on the ingoing light cone formulation for an axially and reflection symmetric spacetime. The solver is second order accurate and was validated in different ways. We use for calibration an auxiliary 1D solver with the same initial and boundary conditions and the same evolution algorithm. We reproduce the quasinormal modes for the massless scalar field harmonics $\ell =0$, $1$ and $2$. For these same harmonics, in the linear approximation, we calculate the balance of energy between the black hole and the world tube. As an example of nonlinear harmonic generation, we show the distortion of a marginally trapped two-surface approximated as a q-boundary and based upon the harmonic $\ell =2$. Additionally, we study the evolution of the $\ell =8$ harmonic in order to test the solver in a spacetime with a complex angular structure. Further applications and extensions are briefly discussed.

13 pages, 11 figures; to appear in Physical Review D. arXiv admin note: text overlap with arXiv:0711.0564

References in corpus (15)

• Evolution of Binary Black Hole Spacetimes
• Accurate Evolutions of Orbiting Black-Hole Binaries Without Excision
• Gravitational wave extraction from an inspiraling configuration of merging black holes
• Critical phenomena in gravitational collapse
• Critical behaviour in gravitational collapse of radiation fluid --- A renormalization group (linear perturbation) analysis ---
• The spherically symmetric collapse of a massless scalar field
• Null cone evolution of axisymmetric vacuum spacetimes
• News from Critical Collapse: Bondi Mass, Tails and Quasinormal Modes
• Black hole excision with matching
• A framework for large-scale relativistic simulations in the characteristic approach
• A numerical relativistic model of a massive particle in orbit near a Schwarzschild black hole
• The 3-dimensional Einstein-Klein-Gordon system in characteristic numerical relativity
• Non-linear harmonic generation in finite amplitude black hole oscillations
• Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method
• Global energy conservation in nonlinear spherical characteristic evolutions

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