This paper is concerned with the structural stability of spherical horizons. By this we mean stability with respect to variations of the second member of the corresponding differential equations, corresponding to the inclusion of the contribution of operators quadratic in curvature. This we do both in the usual second order approach (in which the independent variable is the spacetime metric) and in the first order one (where the independent variables are the spacetime metric and the connection field). In second order, it is claimed that the generic solution in the asymptotic regime (large radius) can be matched not only with the usual solutions with horizons (like Schwarzschild–de Sitter) but also with a more generic (in the sense that it depends on more arbitrary parameters) horizonless family of solutions. It is however remarkable that these horizonless solutions are absent in the restricted (that is, when the background connection is the metric one) first order approach.

本文关注的是球面视界的结构稳定性。这意味着相对于相应微分方程的第二个成员的变化的稳定性，对应于包含二次曲率算子的贡献。我们在通常的二阶方法（其中自变量是时空度量）和一阶方法（其中自变量是时空度量和连接域）中执行此操作。在二阶中，声称渐近状态（大半径）中的通用解不仅可以与具有视界的通常解（如 Schwarzschild-de Sitter）匹配，而且还可以与更通用的解（从某种意义上说，它取决于在更多任意参数上）无水平的解决方案系列。受限（即，当后台连接是度量连接时）一阶方法。