An object cannot be a point. At least, not in Einstein's gravity. The equations of general relativity require that the source of the field, matter, be smeared out in space, not concentrated in an infinitesimal volume. Otherwise, infinities appear in the formulas, and a smooth spacetime cannot be constructed. This ban was rigorously proven by Robert Geroch and Jennie Traschen back in 1987.
Instead of a point, the author of the new work proposes a tube. Not an abstract one, but a physical one: inside it, time flows along a central filament, and space is layered into two-dimensional surfaces. Each such surface is like a membrane with its own tension. The whole structure resembles a layered roll, where the layers are energy and pressure, smoothly varying from the center to the edge. The total gravitational field of such a tube is smooth, without discontinuities.
The most interesting part happens when the tube's radius is taken to zero. With the right tuning of internal parameters, the tube turns into a point, but not a bare one — with an extra term, akin to a self-interaction force. The particle's mass ceases to be a fundamental constant and emerges as a result of the tube's internal geometry. This is not a trick but a direct consequence of how matter is structured at small scales.
The tube proves stable against small deformations: its layers obey the Jacobi equation for timelike surfaces. This approach does not violate the Geroch–Traschen ban and offers a geometrically clean way to describe matter where a point particle is powerless.
The ban on point sources in general relativity is like a traffic rule: if a car became a point, it would occupy all lanes at once and cause a crash, the equations just "don't add up."