#### In short, the **holographic** **principle** states it is the area A of a surface that constrains the amount of information in the bordering regions, and not the volume. The **holographic** **principle** therefore relates information and geometry, and this suggests it's origin must lie in a theory which unifies matter and spacetime.

**Conclusions**

The holographic principle is a remarkable property that seems to be universally valid. It relates the information content of nature to the geometry of spacetime, and therefore it seems that it originates from a yet unknown theory which unifies quantum mechanics and gravity. According to the covariant entropy bound, the amount of information that a region of space can posses is vastly less than the predictions of any current theory. Even more, it is possible that a deeper theory is not local, since the CEB states that entropy on a light-sheet is limited by the area of its boundary surface. Another interesting feature following from the holographic principle is the existence of cosmological screens. These hypersurfaces contain all the information of a spacetime, hence making it possible that our universe is a giant hologram.

Although most systems composed of ordinary matter seemed to obey a stronger bound than the CEB, S < A3/4,counterexamples have been found by Bousso, Freivogel and Leichenauer[2] and thereby confirmed the universality of the CEB. These counterexamples can be divided in mainly two categories: truncated light-sheets and anti-trapped surfaces in open FRW universes. In the case of anti-trapped surfaces, the CEB can approximately be saturated.

New counterexamples were searched in the anisotropic Bianchi model and in the inhomogeneous LTB model. For the considered solutions of those models (except for the elliptic solution of the LTB model) counterexamples were found that are very similar to those of truncated light-sheets or anti-trapped spheres found by Bousso, Freivogel and Leichenauer [2]. One of those examples approximately saturates the CEB. A new kind of counterexample requiring anisotropy was found in the Bianchi model, but the validity of the derivation is not completely certain, since quantum gravitational effects may be important in the regime that was

considered.