Figure 16

Figure 16: By fitting the Fourier transform of an observed signal to a post-Newtonian expansion, one can measure the various post-Newtonian coefficients ψ (m ,m ),k = 0,2,3, 4,6,7 k 1 2 and coefficients of log-terms ψ5l(m1,m2 ) and ψ6l(m1, m2 ). 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 m1m2 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 6 10 M ⊙ 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 ψ0,ψ2 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].  External LinkThe American Physical Society.