Barrow John D
DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Phys Lett B. 2020 Sep 10;808:135643. doi: 10.1016/j.physletb.2020.135643. Epub 2020 Jul 24.
We investigate the consequences for the black hole area of introducing fractal structure for the horizon geometry. We create a three-dimensional spherical analogue of a 'Koch Snowflake' using a infinite diminishing hierarchy of touching spheres around the Schwarzschild event horizon. We can create a fractal structure for the horizon with finite volume and infinite (or finite) area. This is a toy model for the possible effects of quantum gravitational spacetime foam, with significant implications for assessments of the entropy of black holes and the universe, which is generally larger than in standard picture of black hole structure and thermodynamics, potentially by very considerable factors. The entropy of the observable universe today becomes , where , with for a smooth spacetime structure and for the most intricate. The Hawking lifetime of black holes is also reduced.
我们研究了为视界几何引入分形结构对黑洞面积的影响。我们通过围绕史瓦西事件视界的一系列无限递减的相切球体，创建了一个“科赫雪花”的三维球面类似物。我们可以为视界创建一个具有有限体积和无限（或有限）面积的分形结构。这是一个关于量子引力时空泡沫可能效应的玩具模型，对黑洞和宇宙熵的评估具有重要意义，其熵通常比黑洞结构和热力学的标准图景中的熵大，可能大很多。如今可观测宇宙的熵变为 ，其中 ，对于光滑时空结构 ，对于最复杂的情况 。黑洞的霍金寿命也会缩短。
