A carousel doesn't just spin you around in a circle — with each revolution, it also slightly screws itself into the ground. This corkscrew-like motion is the essence of the NUT charge, a special property of spacetime that physicists have been studying since the mid-20th century.
In the new work, researchers revisited old solutions to Einstein's equations describing curved space around rotating objects with such 'screwing' properties. They showed that mass (ordinary gravity) and NUT charge (a magnetic-like addition) are two sides of the same coin. It all depends on how we solve the main equation: one choice gives mass, the other gives NUT charge. It's like translating one phrase into two languages: the meaning is the same, but the words differ.
The most interesting part came when the authors looked at particles with different spins (internal rotation, like a spinning top). It turned out that the 'electric' version of a particle (associated with mass) and the 'magnetic' version (associated with NUT charge) are described by similar formulas. A special function plays a key role in them — the Bessel function. Only the order of this function changes sign: for mass it is positive, for NUT charge it is negative. It's like looking at the same wave but with the binoculars flipped.
In the end, physicists found no convincing evidence that self-dual gravity exists in higher dimensions — a special case where a particle is completely balanced with itself. In four dimensions, this happens and leads to surprising simplifications in calculations. But in worlds with more dimensions, this magic seems to disappear. This means our Universe is unique in this sense. Or we just haven't found the right 'key' to multidimensional doors yet.
as written by the authors arXiv:2607.22938
We revisit Kerr-NUT metrics and related spin-$$s$$ fields in $$D\geq4$$, and study their associated scattering amplitudes. Starting in position space, we highlight the interpretation of mass and (multiple) NUT charges as being associated to distinct solutions of the rotation-deformed radial equation, which is made explicit in Cartesian multi-Kerr-Schild coordinates. This interpretation extends to electromagnetism with magnetic-type charges, and also extends to higher-spin counterparts, in accordance with the classical double or multi copy. We then establish a notion of ``electric-magnetic" duality in higher dimensions, relating mass/electric to NUT/magnetic charges, which generalises the $$D=4$$ case in a novel manner. For $$D\geq6$$, this involves the choice where the multiple magnetic charges are equal. The duality is revealed in momentum space, by the 3-point scattering amplitudes that generate the solutions. For all spins, these amplitudes are constructed from a spin-raising operator $$\mathcal S_\mu$$ and take the form $$\varepsilon^{\mu_1\cdots\mu_s}{\mathcal S}_{\mu_1}\cdots {\mathcal S}_{\mu_s}$$ acting on a scalar seed. The scalar seed of the electric sector is dual to that of the magnetic sector: where the former's rotation dependence resums to a Bessel function $$J_{\frac{D-5}{2}}$$, the latter resums to a Bessel function $$J_{-\frac{D-5}{2}}$$. Finally, we explore the notion of self-duality that arises from this picture. Studying the classical $$2\!\mapsto\!2$$ amplitudes that determine leading-order scattering, we find no evidence of a higher-dimensional analogue of the integrability of $$D=4$$ self-dual gravity.
The Bessel function that surfaced in this work was invented by astronomer Fraunhofer for calculating planetary motion, and now it's even used in JPEG image compression.
In the novel 'Contact' by Carl Sagan, aliens transmit to humans blueprints for a machine that works on principles of multidimensional physics — possibly with similar dualities.