Bowen-York model solution redux

Altas, Emel
Tekin, Bayram
Initial value problem in general relativity is often solved numerically; with only a few exceptions one of which is the "model" solution of Bowen and York where an analytical form of the solution is available. The solution describes a dynamical, time-asymmetric, gravitating system with mass and linear momentum. Here we revisit this solution and correct an error which turns out to be important for identifying the energy-content of the solution. Depending on the linear momentum, the ratio of the non-stationary part of the initial energy to the total ADM energy takes values between [0, 0.592). This non-stationary part is expected to be turned into gravitational waves during the evolution of the system to possibly settle down to a black hole with mass and linear momentum. In the ultra-relativistic case (the high momentum limit), the maximum amount of gravitational wave energy is 59.2% of the total ADM energy. We also give a detailed account of the general solution of the Hamiltonian constraint.


AKKAS, N; ERDOGAN, F (ASME International, 1993-01-01)
The classical wave equation in spherical coordinates is expressed in terms of a residual potential applying the Residual Variable Method. This method essentially eliminates the second derivative of the potential with respect to the radial coordinate from the wave equation. Thus, the dynamic pressure distribution on the surface of a spherical cavity can be studied by considering the cavity surface only. Moreover, the Residual Variable Method, being amenable to ''marching'' solutions in a finite-difference im...
Goal–oriented a posteriori error estimation for Dirichlet boundary control problems
Yücel, Hamdullah (Elsevier BV, 2021-1)
We study goal-oriented a posteriori error estimates for the numerical approximation ofDirichlet boundary control problem governed by a convection diffusion equation withpointwise control constraints on a two dimensional convex polygonal domain. The localdiscontinuous Galerkin method is used as a discretization technique since the controlvariable is involved in a variational form in a natural sense. We derive primal–dualweightederrorestimatesfortheobjectivefunctionalwithanerrortermrepresentingthemismatch in ...
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Kanoğlu, Utku (2006-10-06)
The initial value problem solution of the nonlinear shallow water-wave equations is developed under initial waveforms with and without velocity. We present a solution method based on a hodograph-type transformation to reduce the nonlinear shallow water-wave equations into a second-order linear partial differential equation and we solve its initial value problem. The proposed solution method overcomes earlier limitation of small waveheights when the initial velocity is nonzero, and the definition of the init...
Linearization instability for generic gravity in AdS spacetime
Altas, Emel; Tekin, Bayram (American Physical Society (APS), 2018-1-24)
In general relativity, perturbation theory about a background solution fails if the background spacetime has a Killing symmetry and a compact spacelike Cauchy surface. This failure, dubbed as linearization instability, shows itself as non-integrability of the perturbative infinitesimal deformation to a finite deformation of the background. Namely, the linearized field equations have spurious solutions which cannot be obtained from the linearization of exact solutions. In practice, one can show the failure o...
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Türker, Burhan Lemi (Informa UK Limited, 2011-01-01)
A linear multivariable model has been derived for the estimation of detonation velocity. Then, its two simplified forms, first-order linear models, have been proposed as estimators of detonation velocities of a large population of explosives having different skeletal structures. Then, the models are analyzed mathematically and regression equations are obtained and discussed. The first model possesses two independent variables E/M and density, whereas the second one is based on E/M only. The total energy (E)...
Citation Formats
E. Altas and B. Tekin, “Bowen-York model solution redux,” EUROPEAN PHYSICAL JOURNAL C, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: