The d-Dimensional Cosmological Constant and the Holographic Horizons

This article is dedicated to establishing a novel approach the cosmological constant, in which it treated as an eigenvalue of certain Sturm–Liouville problem. The key this lies proper formulation physically relevant boundary conditions. Our suggestion regard utilize “holographic condition”, under horizon can only bear natural (i.e., non-fractional) number bits information. Under framework, we study general d-dimensional problem and derive formula for discrete spectrum positive energy density vacuum. For particular case two dimensions, resultant be analytically solved degenerate hypergeometric functions, so possible define explicitly self-action potential, determines fields matter model. We conclude by taking look at model fractal horizon, where Bekenstein’s entropy gets replaced Barrow entropy. gives us chance discuss recently realized existence naked singularities D≠3 models.