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The post-Newtonian (PN) hydrodynamic equations are obtained in the (3+1) formalism, which include the 2.5PN order as the reaction due to the quadrupole gravitational radiation. These equations are valid in various slice conditions, while we adopt a kind of transverse gauge condition to determine the shift vector. In particular, we describe methods to solve the 2PN tensor potential which arises from the spatial 3-metric. Our formulaton in the PN approximation using the (3+1) formalism will be useful for numerical computations providing an initial data for the final merging phase of coalescing binary neutron stars which can be treated only by fully general relativistic simulations.

Post-Newtonian hydrodynamic equations using the (3+1) formalism in general relativity