We review the basic definitions and properties of trapped surfaces and discuss them in the context of Kerr–Vaidya line element. Our study shows that the apparent horizon does not exist in general for axisymmetric space–times. The reason being the surface at which the null tangent vectors are geodesics and the surface at which the expansion of such vectors vanishes do not coincide. The calculation of an approximate apparent horizon for space–times that ensure its existence seems to be the only way to get away with this problem. The approximate apparent horizon, however, turned out to be non-unique. The choice of the shear-free null geodesics, at least in the leading order, seems to remove this non-uniqueness. We also propose a new definition of the black hole boundary.

我们回顾了被困曲面的基本定义和属性，并在 Kerr-Vaidya 线元素的背景下讨论它们。我们的研究表明，对于轴对称时空，视界一般不存在。原因是零切向量是测地线的表面与这些向量的扩展消失的表面不重合。计算时空的近似视界以确保其存在似乎是解决这个问题的唯一方法。然而，近似的视地平线被证明是非唯一的。选择无剪切零测地线，至少在前导顺序中，似乎消除了这种非唯一性。我们还提出了黑洞边界的新定义。