Testing spacetime symmetry through gravitational waves from extreme-mass-ratio inspirals

Gravitational-wave glitches: resonant islands and frequency jumps in non-integrable extreme-mass-ratio inspirals

“…We find that at the orbital level, a clear imprint evinces when the test body transverses a resonant island; besides the fact that the rotation number displays a dynamical plateau [31][32][33][34][35][36], the orbital elements undergo rapid changes when the secondary enters the resonant island. We expect that these abrupt manifestations would be smoother when one considers an instantaneous self-force evolution [37][38][39].…”

“…Eqs. (35), and thus the fluxes (36) and (37), are updated every N r cycles for the whole EMRI evolution. To further guarantee numerical accuracy when radiation reaction is included, we calculate the 4-velocity in each update of the fluxes and check its conservation along a geodesic evolution with initial conditions the energy, angular momentum, position and velocity at every update time step.…”

“…where in the limit N → ∞, the sequence (38) converges to ν θ . Generally, integrable systems exhibit a monotonous change in consecutive rotation numbers (rotation curve), while non-integrable systems exhibit plateaus [18,32,36] when the orbit is crossing a Birkhoff island. The rotation curve has been utilized to distinguish whether various EMRI systems have integrable equations of motion (see [31-36, 50, 60]).…”

“…In EMRIs, though, chaotic motion itself is not expected to be a prominent effect, therefore one must search for alternative generic features that clearly distinguish the existence of chaos. It turns out that a solid indicator of non-integrability is the passage through resonant islands [31][32][33][34][35][36].…”

Prospects for determining the nature of the secondaries of extreme mass-ratio inspirals using the spin-induced quadrupole deformation

“…The stellar-mass object (hereafter, the secondary) completes ∼ 10 4 − 10 6 orbits cycles around the supermassive central object (hereafter, the primary) within the LISA frequency band before plunging [17,18]. The gravitational waveform from the system carries very accurate information about the parameters of the binary system [10,19] and the geometry surrounding the primary object [20][21][22][23][24][25][26][27][28]. Recent studies have shown that LISA can measure the mass and spin of the primary with significantly high accuracy as compared to current ground-based detectors and X-ray measurements [10,19].…”