Gravitational waves from equatorially eccentric extreme mass ratio inspirals around swirling Kerr black holes

Abstract

The swirling-Kerr black hole is a novel solution of vacuum general relativity and has an extra swirling parameter characterizing the rotation of spacetime background. We have studied the gravitational waves generated by extreme mass ratio inspirals (EMRIs) along eccentric orbits on equatorial plane in this novel swirling spacetime. Our findings indicate that this swirling parameter leads to a delayed phase shift in the gravitational waveforms. Furthermore, we have investigated effects of the swirling parameter on the potential issue of waveform confusion caused by the orbital eccentricity and semi-latus rectum parameters. As the swirling parameter increases, the relative variations in the eccentricity increase, while the variations in the semi-latus rectum decrease rapidly. These trends of the changes related to the orbital eccentricity and the semi-latus rectum with the swirling parameter resemble those observed with the MOG parameter in the Scalar-Tensor-Vector-Gravity (STVG) theory, but with different rates of change. Furthermore, our results also reveal that effects of the background swirling parameter on the relative variations in the eccentricity and the semi-latus rectum are distinctly different from those of the black hole spin parameter. These results provide deeper insights into the properties of EMRI gravitational waves and the background's swirling.

Figures (8)

• Figure 1: Changes of the periastron shift difference $\Delta\phi_{sK}-\Delta\phi_{K}$ (left panel), the radial period difference $T_{r(sK)}-T_{r(K)}$ (middle panel) and the number of cycles $N$ (right panel) with the swirling parameter $j$ for different $e$, $p$ and $a$.
• Figure 2: Time series of the orbital motion with the orbital parameters $e=0.4$ and $p=7.0M$ in the swirling Kerr spacetime for different $j$. The left panel and the right panel respectively correspond to the motion in the $r$-direction and $\phi$-directions. The top, middle and bottom rows respectively denote $a=0.0$, $a=0.01$ and $a=0.1$.
• Figure 3: Trajectories with the orbital parameters $e=0.4$ and $p=7.0M$ in the swirling Kerr spacetime for different swirling parameters $j$. The left, middle and right panels respectively correspond to cases $a=0$, $a=0.01$ and $a=0.1$.
• Figure 4: The plus component of EMRI waveforms for different swirling parameter $j$. The top, middle and bottom rows respectively correspond to the cases with centre black hole's spin $a=0.0$, $a=0.01$, $a=0.1$. Here, we set the orbital parameters to $e=0.4$ and $p=7.0M$.
• Figure 5: The cross component of EMRI waveforms for different swirling parameter $j$. The top, middle and bottom rows respectively correspond to the cases with centre black hole's spin $a=0.0$, $a=0.01$, $a=0.1$. Here, we set the orbital parameters to $e=0.4$ and $p=7.0M$.