Abstract
AbstractInitial 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.
Publisher
Springer Science and Business Media LLC
Subject
Physics and Astronomy (miscellaneous),Engineering (miscellaneous)
Reference15 articles.
1. B.P. Abbott et al., [LIGO Scientific and Virgo Collaborations] Observation of Gravitational Waves from a Binary Black Hole Merger. Phys. Rev. Lett. 116(6), 061102 (2016)
2. J.M. Bowen, J.W. York Jr., Time asymmetric initial data for black holes and black hole collisions. Phys. Rev. D 21, 2047–2056 (1980)
3. R. Arnowitt, S. Deser, C. Misner, The dynamics of general relativity. Phys. Rev. 116, 1322 (1959)
4. R. Arnowitt, S. Deser, C. Misner, The dynamics of general relativity. Phys. Rev. 117, 1595 (1960)
5. R. Arnowitt, S. Deser, C. Misner, in Gravitation: An Introduction to Current Research ed. by L. Witten (Wiley, New York, 1962)
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