论文标题
D维宇宙常数和全息视野
The d-Dimensional Cosmological Constant and the Holographic Horizons
论文作者
论文摘要
本文致力于建立一种新颖的方法，以解决宇宙学常数，其中将其视为某些sturm--liouville问题的特征值。这种方法的关键在于适当地制定物理相关的边界条件。我们在这方面提出的建议是利用``全息边界条件''，根据该''全息边界条件'，宇宙学的地平线只能具有自然（即非分数）信息的信息。在此框架下，我们研究了一般的D维问题，并得出了真空正能量密度离散光谱的一般公式。对于两个维度的特定情况，可以在退化的高几幅函数中分析解决结果，因此可以明确定义自我行动潜力，从而确定模型中物质的领域。我们通过查看分形范围的D维模型来结束文章，在该模型中，Bekenstein的熵公式被Barrow熵取代。这使我们有机会讨论最近在$ d \ neq 3 $型号中存在裸奇异品的问题。
This article is dedicated to establishing a novel approach to the cosmological constant, in which it is treated as an eigenvalue of a certain Sturm--Liouville problem. The key to this approach lies in the proper formulation of physically relevant boundary conditions. Our suggestion in this regard is to utilize the ``holographic boundary condition'', under which the cosmological horizon can only bear a natural (i.e., non-fractional) number of bits of information. Under this framework, we study the general d-dimensional problem and derive the general formula for the discrete spectrum of a positive energy density of vacuum. For the particular case of two dimensions, the resultant problem can be analytically solved in the degenerate hypergeometric functions, so it is possible to define explicitly a self-action potential, which determines the fields of matter in the model. We conclude the article by taking a look at the d-dimensional model of a fractal horizon, where the Bekenstein's formula for the entropy gets replaced by the Barrow entropy. This gives us a chance to discuss a recently realized problem of possible existence of naked singularities in the $D\neq 3$ models.
