  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.
