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arXiv · 2007.14279

Bowen-York Model Solution Redux

Emel Altas·Bayram Tekin
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Abstract

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.

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Emel Altas, Bayram Tekin. 2020-07-28. Bowen-York Model Solution Redux. https://doi.org/10.1140/epjc%2Fs10052-021-09139-z

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