Scalar perturbations of nonsingular nonrotating black holes in conformal gravity

We study scalar and electromagnetic perturbations of a family of nonsingular nonrotating black hole spacetimes that are solutions in a large class of conformally invariant theories of gravity. The effective potential for scalar perturbations depends on the exact form of the scaling factor. Electromagnetic perturbations do not feel the scaling factor, and the corresponding quasinormal mode spectrum is the same as in the Schwarzschild metric. We find that these black hole metrics are stable under scalar and electromagnetic perturbations. Assuming that the quasinormal mode spectrum for scalar perturbations is not too different from that for gravitational perturbations, we can expect that the calculation of the quasinormal mode spectrum and the observation with gravitational wave detectors of quasinormal modes from astrophysical black holes can constrain the scaling factor and test these solutions.

Figure 1

Dependence of the effective potential of scalar perturbations on the tortoise coordinate for different values (from left to right) of the angular quantum number $\ell$, conformal factor $L$, and the degree $N$. The values of the parameters are given in the plots.

Figure 2

Evolution of scalar perturbations in the nonsingular nonrotating black hole background in conformal gravity as a function of time for different values of the characteristic parameters. Left panel: $\ell =1$, $N=20$. Middle panel: $\ell =1$, $L/M=1.2$. Right panel: $L/M=1.2$, $N=20$. The values of the parameters that are changed are given in the legend of each panel.

Figure 3

Dependence of the $\ell =2$, $n=0$ quasinormal frequencies of the scalar, $s=0$, perturbation on the parameter $L/M$ for the regular nonrotating black hole in conformal gravity for different values of $N$.

Figure 4

Dependence of the $\ell =2$, $n=0$ quasinormal frequencies of scalar, $s=0$, perturbations on the degree $N$ for regular nonrotating black holes in conformal gravity for different values of $L$.

Figure 5

Quasinormal frequencies with $n>0$ for scalar perturbations in nonsingular spherically symmetric black holes in conformal gravity with $L/M=1$ and $N=1$ for several values of the multipole number $\ell$. The overtone number, $n$, increases as $n=0,1,2,\dots$ from bottom to top.