Solving the Darwin problem in the first post-Newtonian approximation of general relativity

Details Solving the Darwin problem in the first post-Newtonian approximation of general relativity Solving the Darwin problem in the first post-Newtonian approximation of general relativity

1997-05-13

arxiv.org/abs/gr-qc/9705027v1

Phys.Rev. D56 (1997) 798-810

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages, revtex, 4 figures(eps), accepted for publication in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.56.798

We analytically calculate the equilibrium sequence of the corotating binary stars of incompressible fluid in the first post-Newtonian(PN) approximation of general relativity. By calculating the total energy and total angular momentum of the system as a function of the orbital separation, we investigate the innermost stable circular orbit for corotating binary(we call it ISCCO). It is found that by the first PN effect, the orbital separation of the binary at the ISCCO becomes small with increase of the compactness of each star, and as a result, the orbital angular velocity at the ISCCO increases. These behaviors agree with previous numerical works.

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