Post‐Newtonian Smoothed Particle Hydrodynamics

We introduce an adaptation of the well known Tree+SPH numerical scheme toPost Newtonian (PN) hydrodynamics and gravity. Our code solves the (0+1+2.5)PNequations. These equations include Newtonian hydrodynamics and gravity (0PN),the first order relativistic corrections to those (1PN) and the lowest ordergravitational radiation terms (2.5PN). We test various aspects of our codeusing analytically solvable test problems. We then proceed to study the 1PNeffects on binary neutron star coalescence by comparing calculations with andwithout the 1PN terms. We find that the effect of the 1PN terms is rathersmall. The largest effect arises with a stiff equation of state for which themaximum rest mass density increases. This could induce black hole formation.The gravitational wave luminosity is also affected.Comment: 28 pages, 13 figures, revised version published in Ap