Quadratic gravity corrections to scalar QNMs of rapidly rotating black holes

Abstract

In an effective-field-theory framework for gravity, black-hole quasinormal mode spectra acquire corrections in quadratic-curvature, scalar-tensor extensions of general relativity. Previous calculations of such corrections were limited to moderate spins, since the corresponding background solutions relied on expansions in the spin parameter. Using recently constructed numerical black-hole solutions valid for large spin, we compute the leading-order deviations from general relativity in the scalar quasinormal mode spectrum of rotating black holes in scalar Gauss-Bonnet and dynamical Chern-Simons gravity. We solve the resulting perturbation equations with pseudo-spectral collocation methods, allowing us to determine the quasinormal-mode corrections for dimensionless spins up to $a/M=0.99$, with accuracy better than $\lesssim 10^{-3}$ for the $l=m=0$ mode and $\lesssim 10^{-6}$ for higher multipoles. For spins $a/M>0.9$, the corrections to certain modes can increase by orders of magnitude.

Figures (5)

• Figure 1: Lowest order corrections $\omega^{(1)}$ to $l=m=0$ scalar QNMs, visualized in the complex plane. Results that were obtained using the spin-expanded background (lines), shown up until $a=0.8$, are compared to results for the spectral background (circles). The circles have a colour-scale to indicate their corresponding spin, going from $a=0$ until $a=0.99$.
• Figure 2: Lowest order corrections to $l=2$ scalar QNMs in sGB for different $m$, visualized in the complex plane. A comparison is made between results (up until $a=0.8$) using spin expansion as background spacetime and results for spins up to $a=0.99$, using the spectral background. The lines show spin expansion results. A dotted line represents $m=-2$, a long dashed line $m=-1$, a full line $m=0$, a short dashed line $m=1$, and a dot dash line $m=2$. Markers show the new results using a numerically calculated background. A star represents $m=-2$, a pentagon $m=-1$, a circle $m=0$, a triangle $m=1$, and a square $m=2.$ The colour denotes the spin of the background black hole, going from $a=0$ until $a=0.99.$
• Figure 3: Lowest order corrections to $l=2$ scalar QNMs in dCS for different $m$, visualized in the complex plane. A comparison is made between results (up until $a=0.8$) using spin expansion as background spacetime and results for spins up to $a=0.99$, using the spectral background. The lines show spin expansion results. A dotted line represents $m=-2$, a long dashed line $m=-1$, a full line $m=0$, a short dashed line $m=1$, and a dot dash line $m=2$. Markers show the new results using a numerically calculated background. A star represents $m=-2$, a pentagon $m=-1$, a circle $m=0$, a triangle $m=1$, and a square $m=2.$ The colour denotes the spin of the background black hole, going from $a=0$ until $a=0.99.$
• Figure 4: Convergence of lowest order correction to $l=m=2$ scalar QNMs as a function of radial grid size. Blue circles represent convergence of the $a=0.05$ case, orange triangles $a=0.5,$ green squares $a=0.9$ and purple stars $a=0.99.$ The corresponding angular grid size of the computations is given by $N_y=N_r-20$.
• Figure 5: Phase space diagram to illustrate which modes seem to diverge in the large-spin limit and which remain well-behaved, along with the DM-ZDM phase boundary in the Eikonal limit (red dashed line). Notably, the modes that exhibit rapid growth in the large-spin regime are the same for sGB and dCS