It is well known that, unlike in higher dimensional general relativity (GR), we cannot have a black hole with an arbitrarily small mass in five dimensional Einstein–Gauss–Bonnet gravity. When we study the dynamical black hole formation via the radiation collapse in the radiating Boulware–Deser spacetime in five dimensions, the central zero mass singularity is weak, conical and naked, and the horizon forms only when a finite amount of matter, that depends on the coupling constant of the Gauss–Bonnet term, falls into the central singularity. To understand this phenomenon transparently and geometrically, we study the radiating Boulware–Deser spacetime in five dimensions using a 1+1+3 spacetime decomposition, for the first time. We find that the geometric and thermodynamic quantities can be expressed in terms of the gravitational mass and the Gauss–Bonnet (GB) parameter and separate each of them into their Gauss–Bonnet and matter parts. Drawing comparisons with five dimensional GR at every step, we explicitly show how the mass gap arises for a general mass function M(v) and what functions for M(v) make certain geometrical quantities well defined at the central singularity. We show in the case of self-similar radiation collapse in the modified theory, the central singularity is not a sink for timelike geodesics and is extendable. This clearly demonstrates how the GB invariant affects the nature of the final state of a continual collapse in this modified theory.

中文翻译：

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五维爱因斯坦-高斯-邦尼特黑洞的质量间隙：几何解释

众所周知，与高维广义相对论（GR）不同，在五维爱因斯坦-高斯-邦尼引力中我们不能拥有任意小质量的黑洞。当我们通过五个维度的辐射布尔韦尔-德瑟时空中的辐射塌缩来研究动态黑洞的形成时，中心零质量奇点是弱的、圆锥形的和裸露的，并且视界仅在物质数量有限时形成，这取决于高斯-邦内项的耦合常数落入中心奇点。为了透明地和几何地理解这种现象，我们首次使用 1+1+3 时空分解研究五个维度的辐射 Boulware-Deser 时空。我们发现几何量和热力学量可以用引力质量和高斯-邦尼特（GB）参数来表达，并将它们分成高斯-邦尼特和物质部分。在每一步中与五维 GR 进行比较，我们明确地展示了一般质量函数的质量间隙是如何产生的中号（v）以及什么功能中号（v）在中心奇点处明确定义某些几何量。我们在修正理论中的自相似辐射塌陷的情况下证明，中心奇点不是类时测地线的汇点并且是可扩展的。这清楚地表明了 GB 不变量如何影响该修正理论中连续崩溃最终状态的性质。