# Synopsis: Post-Minkowski gravity

A “simple” closed-form Hamiltonian for a relativistic system of $n$ gravitating particles, which depends only on the particles’ momenta and coordinates, is developed.

In 1916, shortly after the appearance of the theory of general relativity in essentially its final form, Albert Einstein and others started to work out “post-Newtonian” approximation methods that could be applied to systems where the gravitational field is weak and the velocity of the particles much less than that of light. Similar efforts led to the development of the “post-Minkowski” approximation, in which the field is still assumed to be weak but the particle motion is not necessarily small and can in fact be completely relativistic. Both approximations have been the basis for numerical studies of the gravitational waves emitted by binary black-hole and neutron-star systems—the most promising candidates for gravitational-wave detectors such as LIGO and VIRGO.

Analytic methods are often useful for describing general-relativistic dynamics. In an article appearing in the June 23rd issue of Physical Review Letters, Tomáš Ledvinka, Gerhard Schäfer, and Jiří Bičák, of Charles University in the Czech Republic and the Friedrich-Schiller-Universität in Germany, present a surprisingly simple closed-form, post-Minkowski Hamiltonian for a gravitating $n$-particle system that is fully relativistic and includes all terms linear in the gravitational constant $G$. Although this Hamiltonian does not include higher-order terms in $G$, the “particles” it describes can actually be strong-gravity objects such as black holes. As such, this Hamiltonian may prove useful in future studies of relativistic binary star systems. - Jerome Malenfant

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