准拓扑引力中的一种Fan-Wang型规则黑洞
Fan-Wang type regular black holes in Quasi-Topological Gravity
AI总结：
本文在准拓扑引力中构造了一种无需物质场的高维Fan-Wang型规则黑洞解，通过高阶曲率修正实现规则中心，且在负质量情况下仍保持规则性。
摘要：
我们构建了准拓扑引力（QTG）中任意高维时空（大于四维）中一类Fan-Wang型规则黑洞解。与原始的Fan-Wang解不同，后者是在四维广义相对论耦合非线性电动力学的情况下得到的，我们的高维推广不需要任何物质场。相反，规则性是通过无限多的高曲率修正来实现的。我们通过显式确定每个曲率阶次对应的耦合常数，证明Fan-Wang型度规是QTG场方程的解。在适当的参数范围内，该解描述了一个渐近平坦的黑洞时空，具有规则中心。值得注意的是，即使在负质量的情况下，几何结构仍可以完全保持规则，这与爱因斯坦引力形成鲜明对比。
英文摘要：
We construct a class of regular black hole solutions of the Fan-Wang type within quasi-topological gravity (QTG) in arbitrary spacetime dimensions greater than four. In contrast to the original Fan-Wang solution, which was obtained in four-dimensional general relativity coupled to nonlinear electrodynamics, our higher-dimensional generalization does not require any matter fields. Instead, regularity is achieved purely through an infinite tower of higher-curvature corrections. We demonstrate that the Fan-Wang-type metric is a solution to the QTG field equations by explicitly determining the corresponding coupling constants for each curvature order. Within an appropriate parameter regime, the solution describes an asymptotically flat black hole spacetime with a regular center. Remarkably, even in the case of negative mass, the geometry can remain completely regular, in sharp contrast to Einstein gravity.
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