We first present an overview of the Schwarzschild vacuum spacetime within general relativity, with particular emphasis on the role of scalar polynomial invariants and the null frame approach (and the related Cartan invariants), that justifies the conventional interpretation of the Schwarzschild geometry as a black hole spacetime admitting a horizon (at \(r=2M\) in Schwarzschild coordinates) shielding a singular point at the origin. We then consider static spherical symmetric vacuum teleparallel spacetimes in which the torsion characterizes the geometry, and the scalar invariants of interest are those constructed from the torsion and its (covariant) derivatives. We investigate the Schwarzschild-like spacetime in the teleparallel equivalent of general relativity and find that the torsion scalar invariants (and, in particular, the scalar T) diverge at the putative “Schwarzschild” horizon. In this sense the resulting spacetime is not a black hole spacetime. We then briefly consider the Kerr-like solution in the teleparallel equivalent of general relativity and obtain a similar result. Finally, we investigate static spherically symmetric vacuum spacetimes within the more general F(T) teleparallel gravity and show that if a such a geometry admits a horizon, then the torsion scalar T necessarily diverges there; consequently in this sense such a geometry also does not represent a black hole.

我们首先概述了广义相对论中的史瓦西真空时空，特别强调了标量多项式不变量和零框架方法（以及相关的卡坦不变量）的作用，这证明了将史瓦西几何学的传统解释为黑洞时空承认视界（在 \（r=2M\） 处）在 Schwarzschild 坐标中），在原点处屏蔽一个奇异点。然后，我们考虑静态球对称真空遥并行时空，其中扭转表征了几何结构，而感兴趣的标量不变量是由扭转及其（协变）导数构成的不变量。我们在广义相对论的遥平行等价物中研究了类似施瓦西尔德的时空，发现扭转标量不变量（特别是标量 T）在假定的“史瓦西”视界发散。从这个意义上说，得到的时空不是黑洞时空。然后，我们简要考虑了广义相对论的远平行等价物中的类似 Kerr 的解，并得到了类似的结果。最后，我们研究了更普遍的 F（T） 远平行引力中的静态球对称真空时空，并表明如果这样的几何结构允许一个视界，那么扭转标量 T 必然会在那里发散;因此，从这个意义上说，这样的几何也不代表黑洞。