TY - JOUR

T1 - Gravitational radiation reaction in the Newtonian limit

AU - Futamase, T.

PY - 1983/1/1

Y1 - 1983/1/1

N2 - The asymptotic approximation scheme based on the theory of the Newtonian limit developed in the preceding paper is applied to the gravitational radiation-reaction problem. All divergences encountered in previous approaches disappear: For any the asymptotic approximation is finite to all orders we have calculated, even beyond radiation-reaction order. This is because the divergent terms in previous work were misordered, and make finite contributions to coefficients of lower-order terms in the asymptotic expansion. The logarithmic divergences, in particular, turn up as an 10 ln term in the asymptotic expansion (i.e., between 2.5 and 3 post-Newtonian order) which shows that the relativistic sequence is not C at =0. This does not, however, affect the asymptotic convergence of the approximation. The radiation-reaction terms are used to calculate the period shortening of a nearly-Newtonian binary system directly from the equations of motion, avoiding the well-known difficulties associated with energy in general relativity. It is proved that the prediction derived from the standard quadrupole formula applies in the Newtonian limit. It is also shown that random data for the initial gravitational wave field do not affect the calculation of radiation reaction, even if their amplitude is of first post-Newtonian order.

AB - The asymptotic approximation scheme based on the theory of the Newtonian limit developed in the preceding paper is applied to the gravitational radiation-reaction problem. All divergences encountered in previous approaches disappear: For any the asymptotic approximation is finite to all orders we have calculated, even beyond radiation-reaction order. This is because the divergent terms in previous work were misordered, and make finite contributions to coefficients of lower-order terms in the asymptotic expansion. The logarithmic divergences, in particular, turn up as an 10 ln term in the asymptotic expansion (i.e., between 2.5 and 3 post-Newtonian order) which shows that the relativistic sequence is not C at =0. This does not, however, affect the asymptotic convergence of the approximation. The radiation-reaction terms are used to calculate the period shortening of a nearly-Newtonian binary system directly from the equations of motion, avoiding the well-known difficulties associated with energy in general relativity. It is proved that the prediction derived from the standard quadrupole formula applies in the Newtonian limit. It is also shown that random data for the initial gravitational wave field do not affect the calculation of radiation reaction, even if their amplitude is of first post-Newtonian order.

UR - http://www.scopus.com/inward/record.url?scp=0000809322&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000809322&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.28.2373

DO - 10.1103/PhysRevD.28.2373

M3 - Article

AN - SCOPUS:0000809322

VL - 28

SP - 2373

EP - 2381

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 10

ER -