In recent times there is a surge of interest in constructing Einstein-Gauss-Bonnet (EGB) gravity, in the limit $D \to 4 $, of the $D$-dimensional EGB gravity. Interestingly, the static spherically symmetric solutions in the various proposed $D \to 4 $ regularized EGB gravities coincide, and incidentally some other theories also admit the same solution. We prove a theorem that characterizes a large family of nonstatic or radiating spherically symmetric solutions to the $4D$ EGB gravity, representing, in general, spherically symmetric Type II fluid. An extension of the theorem, given without proof as being similar to the original theorem, generates static spherically symmetric black hole solutions of the theory. It not only enables us to identify available known black hole solutions as particular cases but also to generate several new solutions of the $4D$ EGB gravity.

中文翻译：

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在 4D Einstein-Gauss-Bonnet 引力中生成黑洞

最近，人们对构建爱因斯坦-高斯-博内 (EGB) 引力的兴趣激增，在 $D 维 EGB 引力的极限 $D \ to 4 $ 内。有趣的是，在各种提出的 $D \to 4 $ 正则化 EGB 引力中的静态球对称解是一致的，顺便说一句，其他一些理论也承认相同的解。我们证明了一个定理，该定理表征了 $4D$ EGB 重力的一大类非静态或辐射球对称解，通常代表球对称 II 型流体。定理的扩展，在没有证明的情况下与原始定理相似，生成理论的静态球对称黑洞解。