Binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 60, Issue 12, 1999, Pages

  Schäfer, Gerhard ^b  

^a UNIVERSITY OF BIALYSTOK   (Poland)

^b FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044407509     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.60.124003     Document Type: Article

References (10)

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6. Z. Andrade and R. H. Price, Phys. Rev. D 56, 6336 (1997).
7. The reduced relative position vector (Formula presented) is defined as (Formula presented) together with (Formula presented) and (Formula presented); here (Formula presented) We also introduce the parameter (Formula presented) where (Formula presented) is the reduced mass of the system. As the reduced Hamilton function (Formula presented) we define (Formula presented) (Formula presented) depends on masses of the binary system only through the parameter (Formula presented) From now on the hat will indicate division by the reduced mass (Formula presented)
8. The regularized value of the function f at its singular point (Formula presented) is based on the Hadamard’s “partie finie” regularization. We expand (Formula presented) (where (Formula presented) is a unit vector) into a Laurent series around (Formula presented) (Formula presented) The coefficients (Formula presented) in this expansion depend on the unit vector (Formula presented) The regularized value of the function f at (Formula presented) is the coefficient (Formula presented) averaged over all directions, i.e., (Formula presented) We also always define (Formula presented) More details on the applications of the Hadamard’s regularization can be found in P. Jaranowski, in Mathematics of Gravitation. Part II. Gravitational Wave Detection, edited by A. Królak (Institute of Mathematics, Polish Academy of Sciences, Warszawa, 1997), Vol. 41, Part II, p. 55.
9. L. Infeld and J. Plebański, Motion and Relativity (Pergamon Press, Oxford, 1960), p. 217.
10. T. Kimura and T. Toiya, Prog. Theor. Phys. 48, 316 (1972).