Starting from Padmanabhan's entropy functional, it is shown that the Brown-York tensor (describing energy-momentum on the spacetime boundary) naturally arises as a projection of the canonical momentum onto the normal vectors of the hypersurface. This approach works equally for timelike and lightlike boundaries, shedding light on the asymmetry of the lightlike Brown-York tensor. Moreover, the method is generalized to scalar-tensor theories: it reproduces the equations of motion and explains the non-conservation of boundary energy under non-minimal coupling. The work reveals a deep connection between bulk dynamics and boundary momentum, as in holography.
Gravity isn’t fundamental—it’s a shadow cast by entropy, the measure of disorder. Back in the 1970s, Jacob Bekenstein and Stephen Hawking found that black holes store disorder on their surface, as if information is smeared across the shell. Now physicists have derived Einstein’s equations—the rules by which mass bends spacetime—from entropy density. The same recipe describes energy at boundaries—like the pressure at a black hole’s edge—even for surfaces zipping along at light speed. Before, the math broke down there; now everything snaps into place: chaos inside births geometry outside. Tests with an extra field, a kind of invisible medium, confirmed that this entropic glue holds universally. In an unexpected twist, at lightlike boundaries, energy behaves like a frictionless fluid—it flows but never loses shape.
🎯 A black hole stores information about its disorder on its surface—as if all data is written on the shell, not inside.