Gravitational Wave Glitches in Chaotic Extreme-Mass-Ratio Inspirals

The Kerr geometry admits the Carter symmetry, which ensures that the geodesic equations are integrable. It is shown that gravitational waveforms associated with extreme-mass-ratio inspirals involving a nonintegrable compact object display “glitch” phenomena, where the frequencies of gravitational waves increase abruptly, when the orbit crosses certain spacetime regions known as Birkhoff islands. The presence or absence of these features in data from upcoming space-borne detectors will therefore allow not only for tests of general relativity but also of fundamental spacetime symmetries.

Figure 1

Power spectral density of a Kerr (green), a non-Kerr (red), and a deformed-Kerr (blue) EMRI consisting of a light companion with $\mu =M_{\odot }$ and a supermassive compact object with $M=10^6{M}_{\odot }$ ($\mu /M=10^{-6}$) and $a=0.99M$ at a luminosity distance $d=50\mathrm{M}\mathrm{p}\mathrm{c}$, overplotted on the LISA power spectral density curve with $\mathrm{SNR}=1$ (dashed curve). All small-mass companions begin their inspiral with $E_0=0.95\mu$, $L_{z,0}=3M\mu$ and initial conditions $r(0)=5.70903M,\dot{r}(0)=0.1,\theta (0)=\pi /2$, with the remaining $\dot{\theta }(0)$ being defined by the constraint equation (7) in Ref. [17]. The most prominent Fourier peaks are presented in the enlarged insets, while the remaining peaks correspond to higher harmonics. The evolution time of the EMRI is $t=2\times {10}^{6}M$, which corresponds, roughly, to 3 months of detection. The deformation parameters are ${\alpha }_Q=-1.8$ for the non-Kerr and ${\alpha }_{22}=-2.2$ for the deformed-Kerr inspiral, while for the Kerr inspiral ${\alpha }_Q={\alpha }_{22}=0$.

Figure 2

Periodogram of a deformed-Kerr (left) and a non-Kerr EMRI (right) GW, plotted below the most prominent GW peak, as depicted in the right-hand inset of Fig. 1.