Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist
solutions of the time-symmetric two-black-hole initial value problem are
derived. The static Hamiltonians related to the expanded solutions, after
identifying the bare masses in both solutions, are found to differ from each
other at the third post-Newtonian approximation. By shifting the position
variables of the black holes the post-Newtonian expansions of the three metrics
can be made to coincide up to the fifth post-Newtonian order resulting in
identical static Hamiltonians up the third post-Newtonian approximation. The
calculations shed light on previously performed binary point-mass calculations
at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review
