Regular Article - Theoretical Physics
Bowen–York model solution redux
Department of Physics, Karamanoglu Mehmetbey University, 70100, Karaman, Turkey
2 Department of Physics, Middle East Technical University, 06800, Ankara, Turkey
Accepted: 13 April 2021
Published online: 18 April 2021
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.
© The Author(s) 2021
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