Using the WKB method, we show that the peak location ($r_{\rm peak}$) of the potential, which determines the quasinormal mode frequency of the Kerr black hole, obeys an accurate empirical relation as a function of the specific angular momentum $a$ and the gravitational mass $M$. If the quasinormal mode with $a/M \sim 1$ is observed by gravitational wave detectors, we can confirm the black-hole space-time around the event horizon, $r_{\rm peak}=r_+ +O(\sqrt{1-q})$ where $r_+$ is the event horizon radius. While if the quasinormal mode is different from that of general relativity, we are forced to seek the true theory of gravity and/or face to the existence of the naked singularity.

Gravitational singularity A gravitational singularity (sometimes called a spacetime singularity) is a term used to describe the center of a black hole where gravity is thought to approach infinity.[1] In the center of each black hole is a singularity, a point where infinite density develops as spacetime approaches it. Spacetime goes toward infinite curvature and matter is crushed to infinite density under the pull of infinite gravity. At a singularity, space and time cease to exist as we know them and current laws of physics cannot be applied to this region.[2] Singularities form by a collapse of a star, where star with high enough mass (above 30 times the sun) would shrink under its own gravity and force until it becomes a single, one dimensional point. When it forms, space and time would be infinite in there. An example would be that if a person were to stand on a collapsing star right before the singularity forms, and they sent a signal every second to a nearby observer, time and space would slow down as the singularity is being formed. The observer would hear the signal slowing down. Let's say the singularity forms at 12:00 exactly.

Due to quantum uncertainty, photons won’t actually orbit forever here, however they can still orbit for a long time. For rotating black holes, there are actually many photon spheres, depending on the angle that the photon is going relative to how the black hole is spinning. However, these paths are still unstable, with the exception of the one inside the black hole (which itself most likely would not actually exist due to the mass and energy falling in). Effect on light At the middle of a black hole, there is a gravitational center called a singularity. It is impossible to see into it because the gravity prevents any light escaping. Outside the event horizon, light and matter will still be pulled toward the black hole. If a black hole is surrounded by matter, the matter will form an "accretion disk" around the black hole. An accretion disk looks something like the rings of Saturn, but thicker, bigger, and way brighter. As it gets sucked in, the matter gets very hot and shoots x-ray radiation into space. Think of this as the water spinning around the hole before it falls in, getting vaporized by friction. Most black holes are too far away for us to see the accretion disk and jet.