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Physicists have discovered that certain black holes in higher dimensions possess an exact symmetry where two very different types of waves ring at identical frequencies. The researchers, Davide Batić and Denys Dutykh from Khalifa University in Abu Dhabi, studied nonrotating black holes ranging from five to 26 dimensions. They examined disturbances caused by a scalar field, which acts like a spherical breathing motion, and a dipole twist of spacetime itself. In every dimension from five upward, these two distinct waves produce the same tones, including overtones, provided the Gauss–Bonnet term is not active.

The standard method for calculating these frequencies often fails because the barriers surrounding the black holes become complex with deep dips when extra dimensions are involved. Instead, the team used a Chebyshev spectral method to solve the problem with 300 significant digits of precision. They proved that both wave types share the same spectrum because their barriers are constructed from one underlying curve; squaring this curve and adding its slope creates the first barrier, while squaring it and subtracting the slope creates the second. This structure mirrors supersymmetric quantum mechanics, where partner equations share a spectrum.

This exact symmetry is a property of Einstein’s gravity equations in higher dimensions but breaks immediately when the Gauss–Bonnet term, suggested by string theory, is switched on. The researchers note that while this mathematical coincidence is exact, it likely cannot be heard directly by detectors because extra dimensions are thought to be smaller than a few hundredths of millimeter. Consequently, the observed rings of astronomical black holes behave as four-dimensional objects, whereas these specific high-precision calculations describe much smaller black holes near the length scale of string theory.