Figure 16: By fitting the Fourier transform of an observed signal to a post-Newtonian expansion, one
can measure the various post-Newtonian coefficients and coefficients
of log-terms and . In Einstein’s theory, all the coefficients depend only
on the two masses of the component black holes. By treating them as independent parameters one
affords a test of the post-Newtonian theory. Given a measured value of a coefficient, one can draw
a curve in the – plane. If Einstein’s theory is correct, then the different curves must all
intersect at one point within the allowed errors. These plots show what might be possible with LISA’s
observation of the merger of a binary consisting of a pair of black holes. In the right-hand
plot all known post-Newtonian parameters are treated as independent, while in the left-hand plot
only three parameters and one of the remainingpost-Newtonian parameter are treated as
independent and the procedure is repeated for each of the remaining parameters. The large SNR in
LISA for SMBH binaries makes it possible to test various post-Newtonian effects, such as the tails of
gravitational waves, tails of tails, the presence of log-terms, etc., associated with these parameters.
Left-hand figure adapted from [48], right-hand figure reprinted with permission from [47]. Ⓒ The
American Physical Society.
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