From holography to the geometry of the spacetime

TL;DR

This paper explores how the holographic principle influences spacetime geometry, demonstrating that certain hypersurfaces are non-parabolic and examining implications for Brownian motion and universe models.

Contribution

It establishes a geometric link between the holographic principle and spacetime properties, providing new insights into spacelike hypersurfaces and universe configurations.

Findings

Complete spacelike hypersurfaces are non-parabolic in holographic spacetimes

Implications for Brownian motion behavior on these hypersurfaces

Method to identify universe models violating the holographic principle

Abstract

We show the geometric consequences that the holographic principle has on the spacetime. Namely, we prove that complete spacelike hypersurfaces in a spacetime that satisfies the holographic principle are non-parabolic. This has important consequences on the behaviour of the Brownian motion in these spacelike hypersurfaces, as well as provides a method for finding examples of universes that lead to a violation of this principle.