Kyoto, Japan -- Black holes embody the ultimate abyss. They are the most powerful sources of gravity in the universe, capable of dramatically distorting space and time around them. When disturbed, they begin to "ring" in a distinctive pattern known as quasinormal modes: ripples in space-time that produce detectable gravitational waves.

In events like black hole mergers, these waves can be strong enough to detect from Earth, offering a unique opportunity to measure a black hole's mass and shape. However, precise calculation of these vibrations through theoretical methods has proven a major challenge, particularly for vibrations that are rapidly weakening.

This inspired a team of researchers at Kyoto University to try a new method of calculating the vibrations of black holes. The scientists applied a mathematical technique called the exact Wentzel-Kramers-Brillouin, or exact WKB analysis to carefully trace the behavior of waves from a black hole out into distant space. While this method has long been studied in mathematics, its application to physics -- especially to black holes -- is still a newly developing area.