Holographic screens in ultraviolet self-complete quantum gravity

Abstract: In this paper we study the geometry and the thermodynamics of a holographic screen in the framework of the ultraviolet self-complete quantum gravity. To achieve this goal we construct a new static, neutral, non-rotating black hole metric, whose outer (event) horizon coincides with the surface of the screen. The space-time admits an extremal configuration corresponding to the minimal holographic screen and having both mass and radius equalling the Planck units. We identify this object as the space-time fundamental building block, whose interior is physically unaccessible and cannot be probed even during the Hawking evaporation terminal phase. In agreement with the holographic principle, relevant processes take place on the screen surface. The area quantization leads to a discrete mass spectrum. An analysis of the entropy shows that the minimal holographic screen can store only one byte of information while in the thermodynamic limit the area law is corrected by a logarithmic term.