Post-Newtonian hydrodynamics and post-Newtonian gravitational wave generation for numerical relativity

Statistics – Computation

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Computational Astrophysics, Gravitational Waves, Relativistic Effects, Computerized Simulation, Einstein Equations, Gravitational Collapse, Gravitational Effects, Hydrodynamics

Scientific paper

An approximate formalism is presented for the equations of evolution of a moderately relativistic self-gravitating fluid which takes into account the dominant (quantitative and qualitative) new effects entailed by Einstein's theory. This (first plus second-and-a-half) post-Newtonian scheme is equivalent to known results of the literature, but casts them in an explicitly 'quasi-Newtonian' form, so that it becomes as easy to implement on a computer as a Newtonian-gravity code for nonrelativistic hydrodynamics. This scheme is completed by a corresponding accurate post-Newtonian gravitational waveform extraction formalism which goes beyond the 'standard quadrupole equation' in including the first relativistic corrections to the emission of gravitational radiation in a form which can be easily implemented numerically. The most important quantitative and qualitative characteristics of the three-dimensional gravitational dynamics and wave generation of a wide range of semirelativistic sources can be studied with minimal computer investment.

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