eLISA/NGO will observe highly relativistic coalescences of black hole binaries, and provide exceptionally strong tests of the predictions of General Relativity.
The first type is dynamical tests based on mergers of two massive black holes of similar mass, with masses of up to about 107 M⊙. In the last hours or minutes before coalescence the Signal-to-noise-ratio (SNR) grows very high, sometimes to a thousand, depending on the redshift of the source. Around the moment of coalescence, a massive black hole binary is the most extreme transformer of mass into energy, emitting a luminosity of 1023 L⊙, much higher than that emitted by all the stars in the observable universe. Because the two masses consist of maximally warped vacuum spacetimes moving near the speed of light and interacting strongly with each other, the full nonlinear dynamics of gravitational theory will be tested.
The second type of test involves a black hole of a few solar masses or a neutron star spiralling into a massive black hole, the so-called Extreme Mass Ratio Inspirals (EMRIs) discussed above. The EMRI is, in this context, the best probe of the spacetime geometry around the central dark object to test whether in detail it matches the unique prediction of general relativity for the gravity of a black hole (Kerr metric). About one hundred thousand cycles of the motion will be observable with eLISA/NGO over one year, before merger. The eccentricities of EMRI orbits are expected to be very high initially, and decay to 0.1 to 0.3 until just before merger.
EMRIs will therefore experience periapsis precession at almost the orbital motion rate, and probably rapid Lense-Thirring precession as well. Comparing the phase of the observed gravitational wave signal with the theoretical prediction of General Relativity will reveal whether the central object is indeed the Kerr black hole of General Relativity.