String-inspired gravity splits two exactly matched tones in higher-dimensional black holes

Getting those tones at all took more care than the usual shortcut allows. Each disturbance feels an effective barrier around the black hole, and the shape of that barrier sets the tones ^[5]. The standard WKB approximation treats the barrier as one smooth hump. With the Gauss-Bonnet term switched on, some barriers develop deep dips and intricate shapes, and the approximation can no longer be trusted ^[5].

So the pair used a Chebyshev spectral method. It maps the whole region outside the black hole onto a finite interval, expands the wave in polynomials and solves the result as a large matrix eigenvalue problem, here to 300 significant digits ^[6]. The precision is how they told real tones from artifacts. A genuine tone stays put as the resolution rises, while a numerical ghost wanders ^[7]. They ran this across 22 spacetime dimensions, five through 26 ^[1], the top value being the number bosonic string theory requires ^[2]. Each black hole was disturbed with a scalar field and with two families of spacetime ripples, one that twists space and one that stretches and squeezes it ^[3].

The proof of the match is short. The barrier for a scalar field's spherical breathing and the barrier for spacetime's simplest twist look nothing alike, and one dips below zero near the black hole ^[8]. Yet both come from one curve: square it and add its slope for one barrier, square it and subtract the slope for the other ^[9]. Physicists know this construction from supersymmetric quantum mechanics, where two partner equations built this way share their spectrum ^[9].

The Gauss-Bonnet term is built from spacetime curvature, and some string theories add it to Einstein's equations at low energies ^[4]. In four dimensions it leaves gravity unchanged; it acts only when there are more ^[4]. "The symmetry belongs to Einstein's theory, not to its string-inspired extension," one of the two authors wrote in a phys.org account of the work ^[2].

The authors attach their own caveat to the match. In Einstein's theory the dipole twist describes a black hole that has been set gently spinning, and it does not radiate on its own ^[10]. "But exact coincidences rarely come for free, and this one is a hidden symmetry of Einstein's equations in higher dimensions," the same author wrote ^[1].

Ringdown tones depend only on a black hole's mass, its spin and the law of gravity, and detectors have been listening for them since 2015 ^[14]. That is why ringing is attractive as a test of modified gravity. Here the size of the objects gets in the way. On whether any of this could be heard, the author's answer was brief: "Not directly." ^[3]

In my view the proven match is the more durable result, because it is exact and holds in every dimension from five upward ^[8]. The split is real but, as reported, qualitative. The thing this account doesn't tell you is how far apart the two sets of tones move for a given strength of the Gauss-Bonnet correction ^[11].