Phys. Rev. D 56, 798–810 (1997)Solving the Darwin problem in the first post-Newtonian approximation of general relativityReceived 14 February 1997; published in the issue dated 15 July 1997 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 a 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. © 1997 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.56.798
DOI:
10.1103/PhysRevD.56.798
PACS:
04.30.Db, 04.25.Nx
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