Based on Padmanabhan's entropy functional, originally introduced to derive Einstein's equations and demonstrate the emergent nature of gravity, its applicability in a broader context is shown. Using the same entropy density, it is established that the Brown-York tensor naturally emerges as a projection of the canonical momentum conjugate to the normal vectors of the hypersurface. This construction is unified for timelike and lightlike boundaries and explains the structural differences of the lightlike tensor, including its asymmetry. The analysis is extended to scalar-tensor theories: the entropic formulation reproduces the equations of motion and the corresponding Brown-York tensor, and also clarifies its non-conservation under non-minimal coupling with an additional scalar field. The results provide a consistent variational description of quasi-local gravitational quantities and reveal a general structure linking bulk dynamics with boundary momentum.
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.