论文标题
模糊和离散的黑洞模型
Fuzzy and discrete black hole models
论文作者
论文摘要
使用量子riemannian几何形状，我们在4D中求解了ricci = 0静态球体对称溶液，每个$ s^2 $在每个$ t，r $ a r $ a r $ a r $ a a r $ a n of commutative模糊球体中，找到尺寸跳跃，与解决方案的溶液相比，具有时间和辐射形式的5D Tangherlini Blackhoh孔。因此，即使是少量的角度非核电性也会导致根本不同的径向行为，从而改变了拉普拉斯主义者和弱重力极限。同样，我们提供一个3D黑洞的版本，每个$ t，r $现在是$ s^1 $，现在是一个离散的圆$ \ bbb z_n $，带有经典4D Schwarzschild Black Black Hole的时间和径向形式，远离地平线。我们研究laplacian和经典限制$ \ bbb z_n \ to s^1 $。我们还研究了$ \ bbb r \ times s^2 $的3D FLRW模型，其中$ s^2 $是扩展模糊的球体，发现扩展的Friedmann方程是封闭的$ \ bbb r \ bbb r \ bbb r \ times s^3 $宇宙的经典4D。
Using quantum Riemannian geometry, we solve for a Ricci=0 static spherically-symmetric solution in 4D, with the $S^2$ at each $t,r$ a noncommutative fuzzy sphere, finding a dimension jump with solutions having the time and radial form of a classical 5D Tangherlini black hole. Thus, even a small amount of angular noncommutativity leads to radically different radial behaviour, modifying the Laplacian and the weak gravity limit. We likewise provide a version of a 3D black hole with the $S^1$ at each $t,r$ now a discrete circle $\Bbb Z_n$, with the time and radial form of the inside of a classical 4D Schwarzschild black hole far from the horizon. We study the Laplacian and the classical limit $\Bbb Z_n\to S^1$. We also study the 3D FLRW model on $\Bbb R\times S^2$ with $S^2$ an expanding fuzzy sphere and find that the Friedmann equation for the expansion is the classical 4D one for a closed $\Bbb R\times S^3$ universe.
