Quasinormal modes of the Kerr-Newman black hole: GW150914 and fundamental physics implications

We develop an analytical ringdown waveform model, including both the fundamental and the overtone quasinormal modes, for charged black holes and show that it is precise enough to analyze current gravitational wave data. Applying this waveform model to GW150914, the charge to mass ratio of the remnant black hole (${\lambda }_f$) has been constrained with the sole ringdown gravitational wave data for the first time and the 90% upper limit is ${\lambda }_f\le 0.38$. Correspondingly, the deviation parameter of the scalar-tensor vector gravity (${\alpha }_{\mathrm{s}}$) is limited to be ${\alpha }_{\mathrm{s}}\le 0.17$. Our approach can be directly applied to other binary black hole mergers with loud ringdown radiation.

Figure 1

Distribution of mismatch over final charge and final mass, assuming that ${\lambda }_f={\chi }_f$. The black lines represent contours on the mismatch between the NR waveform and our Kerr-Newman waveform.

Figure 2

Mismatch ranges over ${\chi }_f$, assuming $M_f=100M_{\odot }$. The horizontal dashed gray line marks the mismatch at 0.005. We consider the fundamental mode with zero overtone (dashed red), one overtone (dotted blue), two overtones (dash dotted cyan), and higher mode $l=m=3$ (bold green). The purple curve represents a special case that ${\lambda }_f=0.4$ for the fundamental mode in the Kerr-Newman ringdown waveform, other parameters are the same as that in standard Kerr waveform. These two ringdown waveform models match better when more overtones are included.

Figure 3

Posterior distributions of final mass and final spin for GW150914. All of the contours are 90% credible regions. The 1D marginalized posterior distributions for final mass and final spin are shown in the top and right-hand panels respectively. The red solid contour represents the result of using imrphenompv2 model [48], published by LIGO-Virgo collaboration (LVC) [39]. The analysis using standard Kerr ringdown waveform is represented by dashed blue contour. For the Kerr-Newman ringdown waveform model, the distributions are similar for both ${\lambda }_f=0$ (dotted green) and ${\lambda }_f\ne 0$ (dash dotted black).

Figure 4

${\lambda }_f$ and ${\chi }_f$ inferred with one overtone, using data starting at peak strain amplitude. The purple color map represents the joint posterior distribution. The solid curves enclose 68% and 95% of the probability mass. The top and right-hand panels show 1D posteriors for ${\lambda }_f$ and ${\chi }_f$, respectively. The dashed vertical blue lines represent the median value and 90% credible region of ${\lambda }_f$ and ${\chi }_f$.