Three Quantum-Inspired Black Hole Cores Would Ring at Different Pitches, Math Shows
Khalifa University researchers computed how Planck stars, Bonanno-Reuter and Hayward black holes would sound compared with Einstein's, though today's detectors cannot hear the difference.
When two black holes merge, the remnant rings like a struck bell, and the tones of that ringing depend on what the black hole is. A trio of papers by Denys Dutykh, Davide Batic and Fabio Scardigli now shows that three leading proposals for removing the infinite-density core of a black hole would each ring differently from the version in Einstein's general relativity.
Dutykh, an associate professor at Khalifa University of Science and Technology in Abu Dhabi, wrote up the results in a Science X Dialog piece published October 9. The three papers appeared in The European Physical Journal C, Physical Review D and Physics of the Dark Universe. They study so-called quasinormal modes, the characteristic frequencies and decay rates of a black hole's ringdown, for Planck stars, Bonanno-Reuter black holes and Hayward black holes. Each replaces the central singularity with a quantum-inspired core where gravity weakens or changes character at short distances.
Instead of the common WKB approximation, the team used a Chebyshev spectral method running in 200-digit arithmetic. On a standard Einstein black hole it reproduces the known tones to six decimal places, and the group has put its codes and spectra on GitHub.
Measured against an Einstein black hole of the same mass, the results go in opposite directions. A Planck star of one Planck mass has a main tone about 25.0% lower and fades about 21.6% faster, ringing for 1.9 oscillations instead of 3.1. Its light ring, the orbit where light circles the hole, moves outward from 3 to 4.14 mass units. The extreme Bonanno-Reuter black hole, at 3.50 Planck masses, has a main tone about 12.0% higher that fades about 22.3% more slowly, lasting 4.4 oscillations. The extreme Hayward black hole, with core parameter 32/27, has a tone about 9.5% higher, rings about 28% longer at 4.3 oscillations, and has a light ring that moves inward from 3 to 2.65 mass units.
As a cross-check, the extreme Hayward case shows electromagnetic tones rising about 8.0% and fading about 17.9% more slowly, matching the direction seen for gravitational waves. Using an alternative model of how the core responds to gravitational waves lowers the pitch shift to about 6% from 9%.
The pattern is simple. Weaker gravity at short distances raises the pitch and lengthens the ringing, while stronger gravity lowers the pitch and shortens it. The shifts arise because the ringing is generated near the light ring, so changes to the geometry there show up in the sound.
There is a catch. The effects become significant only for black holes with masses near the Planck scale, roughly tens of micrograms. For a black hole with the mass of the Sun, the first paper estimates the change is smaller than one part in 10 to the power 76, far beyond anything current detectors can see. The work is a map of what to look for rather than a detection. "The center of a black hole may stay hidden forever, but its ringing need not keep the secret," Dutykh wrote.
