Is the Equivalence Principle violated by Generalized Uncertainty Principles and Holography in a brane-world?

TL;DR

This paper investigates whether the holographic principle remains valid in models with extra dimensions when considering generalized uncertainty principles, revealing a potential violation of the equivalence principle.

Contribution

It demonstrates that holographic counting can be preserved in extra-dimensional models only if the equivalence principle is violated for point-like sources.

Findings

Holographic scaling can be maintained with extra dimensions.

Violation of the equivalence principle is necessary for consistency.

Inertial and gravitational masses differ in the proposed models.

Abstract

It has been recently debated whether a class of generalized uncertainty principles that include gravitational sources of error are compatible with the holographic principle in models with extra spatial dimensions. We had in fact shown elsewhere that the holographic scaling is lost when more than four space-time dimensions are present. However, we shall show here that the validity of the holographic counting can be maintained also in models with extra spatial dimensions, but at the intriguing price that the equivalence principle for a point-like source be violated and the inertial mass differ from the gravitational mass in a specific non-trivial way.