The Post-Newtonian Equations of Hydrodynamics in General Relativity.

Concepts

Natural SciencesPhysicsFluid MechanicsMathematical PhysicsRelativityAstrophysical Fluid DynamicsEinstein Field EquationsGeneral RelativityMathematical RelativityNewtonian GravityPost-newtonian GravityAngular Momentum ConservationConservation LawsEnergy In General RelativityEquations Of Motion In General RelativityMass In General RelativityPost-newtonian Equations Of MotionPost-newtonian HydrodynamicsVirial Theorem

TL;DR

The study extends the standard Eulerian hydrodynamic equations to include all order‑1/c² corrections consistent with Einstein’s field equations. The authors derive the post‑Newtonian equations of motion together with a tensor form of the virial theorem. These equations admit integrals of motion identical to the Newtonian conservation laws for mass, momentum, angular momentum, and energy, providing a consistent definition of these quantities in the post‑Newtonian framework. Published in The Astrophysical Journal (Nov 1965), DOI 10.1086/148432, Bibcode 1965ApJ…142.1488C.

Abstract

view Abstract Citations (314) References (9) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS The Post-Newtonian Equations of Hydrodynamics in General Relativity. Chandrasekhar, S. Abstract The standard Eulerian equations of hydrodynamics are generalized to take into account, consistently with Einstein's field equations, all effects of order 1/c2. It is further shown that these post-Newtonian equations allow integrals of motion which are entirely analogous to the Newtonian integrals that express the conservation of mass, linear momentum, angular momentum, and energy. The continued validity of these conservation laws enables a consistent definition of "mass," "momentum," and "energy" in the framework of the post-Newtonian theory. Besides the equations of motion, an appropriate tensor form of the virial theorem is also derived. Publication: The Astrophysical Journal Pub Date: November 1965 DOI: 10.1086/148432 Bibcode: 1965ApJ...142.1488C full text sources ADS |