§ 愛因斯坦的廣義相對論在1915年11月完成 ，兩個月內Karl Schwarzschild解出愛因斯坦場方程(Schwarzschild solution)
決定了非旋轉點微塵時空幾何的精確解 ，然後歷經48年才得到Kerr 解 。
Curvature properties of interior black hole metric by Ryszard Deszcz Abdulvahid H. Hasmani Vrajeshkumar G. Khambholja Absos A. Shaikh
A spacetime is a connected 4-dimensional semi-Riemannian manifold endowed with a metric g with signature (− + ++).
時空的幾何由度量張量g與里奇張量S來描述,whereas(然而) the energy momentum tensor 描述時空的物理內涵.
Einstein’s field equations relate g, S and the energy momentum tensor and describe the geometry and physical contents of the spacetime.
By solving Einstein’s field equations for empty spacetime (i.e. S = 0) for a non-static(非靜態) spacetime metric, one can obtain the interior black hole solution, known as the interior black hole spacetime which infers(推論)that a remarkable change occurs in the nature of the spacetime, namely, the external spatial radial(徑向)and temporal coordinates exchange their characters to temporal and spatial coordinates, respectively, and hence the interior black hole spacetime is a non-static one as the metric coefficients are time dependent.
For the sake of mathematical generalizations, in the literature, there are many rigorous geometric structures constructed by imposing the restrictions to the curvature tensor of the space involving first order and second order covariant differentials of the curvature tensor.
Hence a natural question arises that which geometric structures are admitted by the interior black hole metric.
黑洞的研究：
先看一段影片Christopher Reynolds [年輕天文學家講座] [The Stability of Black Holes with Matter]
AMS中有一篇可供參考 [stable black holes in vacuum and beyond] by Elena Giorgi 是王慕道的學生 [ResearchGate]
Roy Kerr Christopher Reynolds Barrett O'Neill Elena Giorgi
| Non-rotating J=0 | Rotating | |
| uncharged (Q=0) | Schwarzschild | Kerr |
| chargedd | Reissner-Nordstrom | Kerr-Newman |