An endless ocean where every wave carries information about what happens in the depths. That is roughly how our Universe works under the holographic principle: the physics inside a volume can be described by processes on its boundary. The authors of the new work took three-dimensional gravity with a negative cosmological constant (which acts as an 'anti-foaming agent,' preventing space from collapsing) and showed that on open boundaries it can be represented as a fluid flow.
Using an exact fluid/gravity correspondence, the physicists derived a closed radial flow equation for the quasilocal stress tensor — a quantity describing the distribution of energy and momentum near the boundary. This equation turned out to be a realization of the so-called holographic $T\bar T$ deformation at a finite cutoff. If you cut off space at some distance from the center, additional stresses appear on the resulting surface, obeying a strict mathematical law. The scientists then applied the inverse scattering method, a technique originally developed to study waves in nonlinear media, to describe the boundary dynamics. They determined which spectral data correspond to gravitational objects and analyzed how the deformation changes soliton solutions (stable solitary waves).
Interestingly, although the boundary system's evolution is governed by an integrable bi-Hamiltonian hierarchy, a dual mathematical structure that guarantees exact solvability, the radial flow itself is not Hamiltonian with respect to the canonical Poisson bracket. In other words, the 'river' of gravitational stresses flows according to rules that do not reduce to simple energy conservation in the usual sense. This work unifies integrability, quasilocal gravitational observables, inverse scattering, and holography with a finite cutoff into a single framework — all on open boundaries, where familiar notions of closed surfaces break down. Thus, the ocean of information at the edge of the Universe continues to tell about its depths.
The term 'holographic principle' comes from optics: a hologram is a two-dimensional plate that, when illuminated, creates a three-dimensional image. Similarly, here: all information about a three-dimensional world can be stored on its two-dimensional boundary.
In Peter Watts's novel 'Blindsight,' an alien life form uses holographic principles for information processing, echoing the idea of encoding the physics of a volume on its surface.