Gravitation, holographic principle, and extra dimensions

TL;DR

This paper explores a holographic interpretation of gravity involving extra dimensions, suggesting a minimum distance for particle individuality and implications for quantum gravity and high-density astrophysical objects.

Contribution

It extends the holographic principle to extra dimensions, proposing a minimum distance for particle distinction and linking gravity, quantum effects, and higher-dimensional theories.

Findings

Stable circular orbits relate to surface paths under tidal gravity.

Existence of a minimum distance where particles lose individuality.

Particles may unify with the central body below this threshold.

Abstract

Within the context of Newton's theory of gravitation, restricted to point-like test particles and central bodies, stable circular orbits in ordinary space are related to stable circular paths on a massless, unmovable, undeformable vortex-like surface, under the action of a tidal gravitational field along the symmetry axis. An interpretation is made in the light of a holographic principle, in the sense that motions in ordinary space are connected with motions on a selected surface and vice versa. Then ordinary space is conceived as a 3-hypersurface bounding a $n$-hypervolume where gravitation takes origin, within a $n$-hyperspace. The extension of the holographic principle to extra dimensions implies the existence of a minimum distance where test particles may still be considered as distinct from the central body. Below that threshold, it is inferred test particles lose theirs individuality and "glue" to the central body via unification of the four known interactions and, in addition, (i) particles can no longer be conceived as point-like but e.g., strings or membranes, and (ii) quantum effects are dominant and matter turns back to a pre-big bang state. A more detailed formulation including noncircular motions within the context of general relativity, together with further knowledge on neutron stars, quark stars and black holes, would provide further insight on the formulation of quantum gravity.