arXiv subjects

R. Takahashi

Publications and source records attributed to R. Takahashi.

23 records · Page 2Linked to original sources

arXiv2003

The coalescence remnant of spinning binary black holes

We compute the gravitational radiation generated in the evolution of a family of close binary black hole configurations, using a combination of numerical and perturbative approximation methods. We evolve the binaries with spins, $s$, aligned or counter-aligned with the orbital angular momentum from near the innermost stable circular orbit (ISCO) down to the final single rotating black hole. For the moderately spinning holes studied here the remnant Kerr black hole formed at the end of an inspiral process have a rotation parameter $a/M\approx0.72+0.32(s/m_H)$, suggesting it is difficult (though not excluded) to end up with near maximally rotating holes from such scenarios.

astro-ph↗

arXiv2002

Modeling gravitational radiation from coalescing binary black holes

With the goal of bringing theory, particularly numerical relativity, to bear on an astrophysical problem of critical interest to gravitational wave observers we introduce a model for coalescence radiation from binary black hole systems. We build our model using the "Lazarus approach", a technique that bridges far and close limit approaches with full numerical relativity to solve Einstein equations applied in the truly nonlinear dynamical regime. We specifically study the post-orbital radiation from a system of equal-mass non-spinning black holes, deriving waveforms which indicate strongly circularly polarized radiation of roughly 3% of the system's total energy and 12% of its total angular momentum in just a few cycles. Supporting this result we first establish the reliability of the late-time part of our model, including the numerical relativity and close-limit components, with a thorough study of waveforms from a sequence of black hole configurations varying from previously treated head-on collisions to representative target for ``ISCO'' data corresponding to the end of the inspiral period. We then complete our model with a simple treatment for the early part of the spacetime based on a standard family of initial data for binary black holes in circular orbit. A detailed analysis shows strong robustness in the results as the initial separation of the black holes is increased from 5.0 to 7.8M supporting our waveforms as a suitable basic description of the astrophysical radiation from this system. Finally, a simple fitting of the plunge waveforms is introduced as a first attempt to facilitate the task of analyzing data from gravitational wave detectors.

astro-ph↗

arXiv2002

New conformally flat initial data for spinning black holes

We obtain an explicit solution of the momentum constraint for conformally flat, maximal slicing, initial data which gives an alternative to the purely longitudinal extrinsic curvature of Bowen and York. The new solution is related, in a precise form, with the extrinsic curvature of a Kerr slice. We study these new initial data representing spinning black holes by numerically solving the Hamiltonian constraint. They have the following features: i) Contain less radiation, for all allowed values of the rotation parameter, than the corresponding single spinning Bowen-York black hole. ii) The maximum rotation parameter $J/m^2$ reached by this solution is higher than that of the purely longitudinal solution allowing thus to describe holes closer to a maximally rotating Kerr one. We discuss the physical interpretation of these properties and their relation with the weak cosmic censorship conjecture. Finally, we generalize the data for multiple black holes using the ``puncture'' and isometric formulations.

gr-qc↗

arXiv2001

Plunge waveforms from inspiralling binary black holes

We study the coalescence of non-spinning binary black holes from near the innermost stable circular orbit down to the final single rotating black hole. We use a technique that combines the full numerical approach to solve Einstein equations, applied in the truly non-linear regime, and linearized perturbation theory around the final distorted single black hole at later times. We compute the plunge waveforms which present a non negligible signal lasting for $t\sim 100M$ showing early non-linear ringing, and we obtain estimates for the total gravitational energy and angular momentum radiated.

gr-qc↗

arXiv1999

Symmetry without Symmetry: Numerical Simulation of Axisymmetric Systems using Cartesian Grids

We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y \neq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.

gr-qc↗