  We revisit the three-body problem in the framework of general relativity. The
Newtonian N-body problem admits choreographic solutions, where a solution is
called choreographic if every massive particles move periodically in a single
closed orbit. One is a stable figure-eight orbit for a three-body system, which
was found first by Moore (1993) and re-discovered with its existence proof by
Chenciner and Montgomery (2000). In general relativity, however, the periastron
shift prohibits a binary system from orbiting in a single closed curve.
Therefore, it is unclear whether general relativistic effects admit a
choreographic solution such as the figure eight. We carefully examine general
relativistic corrections to initial conditions so that an orbit for a
three-body system can be closed and a figure eight. This solution is still
choreographic. This illustration suggests that the general relativistic N-body
problem also may admit a certain class of choreographic solutions.
