1 | In this article Greek indices take the values ![]() ![]() ![]() ![]() |
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2 | The TT coordinate system can be extended to the near zone of the source as well; see for instance Ref. [95]. | |
3 | Let us mention that the 3.5PN terms in the equations of motion are also known, both for point-particle
binaries [85![]() ![]() ![]() ![]() ![]() |
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4 | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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5 | Our notation is the following: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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6 | The constancy of the center of mass ![]() ![]() ![]() |
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7 | This assumption is justified because we are ultimately interested in the radiation field at some given finite
post-Newtonian precision like 3PN, and because only a finite number of multipole moments can contribute at
any finite order of approximation. With a finite number of multipoles in the linearized metric (26![]() ![]() ![]() ![]() ![]() ![]() |
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8 | The ![]() ![]() |
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9 | In this proof the coordinates are considered as dummy variables denoted ![]() ![]() |
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10 | Recall that in actual applications we need mostly the mass-type moment ![]() ![]() |
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11 | This function approaches the Dirac delta-function (hence its name) in the limit of large multipoles:
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12 | An alternative approach to the problem of radiation reaction, besides the matching procedure, is to work only within a post-Minkowskian iteration scheme (which does not expand the retardations): see, e.g., Ref. [43]. | |
13 | At the 3PN order (taking into account the tails of tails), we find that ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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14 | The computation of the third term in Eq. (100![]() ![]() ![]() |
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15 | The function ![]() ![]() ![]() ![]() |
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16 | Eq. (106![]() ![]() ![]() ![]() ![]() |
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17 | It has been possible to “integrate directly” all the quartic contributions in the 3PN metric. See the terms composed of
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18 | It was shown in Ref. [22![]() ![]() |
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19 | The constants ![]() ![]() ![]() ![]() ![]() ![]() |
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20 | Notice also the dependence upon ![]() ![]() ![]() |
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21 | Note that in the result published in Ref. [60![]() ![]() |
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22 | Actually, in the present computation we do not need the radiation-reaction 2.5PN terms in these relations; we give them only for completeness. | |
23 | When computing the gravitational-wave flux in Ref. [26![]() ![]() ![]() ![]() ![]() |
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24 | Notice the strange post-Newtonian order of this time variable: ![]() |
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