Bowen-York Model Solution Redux

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.

arXiv comment10 pages, matches the improved, published version

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• Observation of Gravitational Waves from a Binary Black Hole Merger
• The Dynamics of General Relativity
• 3+1 Formalism and Bases of Numerical Relativity
• A new geometric invariant on initial data for Einstein equations
• Non-stationary Energy in General Relativity
• Generalized Bowen--York Initial Data
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Cited by in corpus (3)

• Approximate analytical description of apparent horizons for initial data with momentum and spin
• Basics of Apparent Horizons in Black Hole Physics
• Perturbative solution of the Einstein Constraints with Spin and Momentum Far Away From a Binary Source in the Bowen-York formalism