Quasinormal modes of spontaneous scalarized Kerr black holes

Abstract

Recent studies have shown that rotating black holes can undergo spontaneous scalarization, leading to deviations from general relativity in the strong-field regime. We present the first nonperturbative calculation of the quasinormal modes (QNMs) of scalarized Kerr black holes in Einstein-scalar-Gauss-Bonnet gravity, without assuming small spin or weak coupling. Our results reveal a universal splitting of the fundamental $l=m=2$ mode into axial-led, polar-led, and scalar-led branches, breaking the isospectrality characteristic of Kerr black holes. This splitting offers distinct signatures in the ringdown phase of gravitational wave signals and provides a new avenue to test gravity in the strong-field regime. Our findings open the possibility of probing beyond-GR physics using precision measurements of black hole ringdowns in upcoming gravitational wave observations.

Figures (3)

• Figure 1: The migration of the $l=m=2$ fundamental mode (dashed lines) for scalarized static BHs on the complex plane with increasing $\lambda/M$ described by the direction of arrows. The black (green) crosses denotes the mode for the gravitational perturbation (the scalar perturbation) at $\lambda=0$. As $\lambda/M$ increases, the gravitational mode of the vacuum BH remains unchanged, and the scalar mode varies as depicted by the green solid line. Scalarized BHs branch from the threshold of nonvanishing $\lambda/M \approx 1.704$, and hence the scalar mode for the scalarized branch (the green dashed line) emerges from the green solid line at the point $\omega \approx 0.4661- 0.0988 i$, instead the green cross (about $0.4836-0.0968 i$). The other dashed lines describe gravitational modes (axial-led modes (blue) and polar-led modes (yellow)) branching from the black cross, where $\lambda/M$ ranges from $1.704$ to $6$. These results exhibit the resemblance of the perturbative response between the vacuum BH and the scalarized BH at the threshold, analogous to their thermodynamic behavior Doneva:2017bvd.
• Figure 2: The spectrum of the fundamental $l=|m|=2$ QNMs for scalarized Kerr BHs are depicted while varying BH spin $\chi$ and fixing the coupling constant $\lambda/M = 1.75$. The left panel shows the real part of the QNMs with varying spin, while the right panel displays the imaginary part. Solid and hollow markers represent the prograde and retrograde mode of the scalarized BHs, respectively. The different colors of markers corresponding to different modes are listed in the legend within the right panel. For comparison, the grey dashed line show the prograde modes of Kerr BHs with $m=2$, while the retrograde modes with $m=-2$ are depicted by the grey solid line. From the right panel, the prograde families always dominate the spectrum as the mode with smallest imaginary part, analogous to the spectrum of Kerr BHs (the grey dashed line is always larger than the grey solid line). However, the polar prograde modes (the yellow solid markers) remarkably exhibit a smaller imaginary part than the polar retrograde mode (the purple hollow markers).
• Figure 3: The $l=m=2$ prograde modes with varying dimensionless coupling constant $\lambda/M$ for rotating scalarized BHs with different spin. The different markers denote the axial modes (blue circles), the polar modes (yellow squares) and the green modes (green diamonds), respectively, as listed in the small frame within the left bottom and held to the remaining panels. The black crosses represent the $l=m=2$ gravitational modes of Kerr BHs with following spin. The three values ($\chi=0.2,0.4,0.6$) of the fixed BH spin are shown at the top of the three column. For each column, the first row displays the real part of QNMs, while the second row shows the imaginary parts. These plots illustrate the emergence of the polar and axial modes for scalarized BHs from the gravitational modes of Kerr BHs at the critical $\lambda/M$. As $\lambda/M$ increases, the polar and axial modes split from each other into two distinct line.