We study a host of spacetimes where the Weyl curvature may be expressed algebraically in terms of an Abelian field strength. These include Type D spacetimes in four and higher dimensions which obey a simple quadratic relation between the field strength and the Weyl tensor, following the Weyl spinor double copy relation. However, we diverge from the usual double copy paradigm by taking the gauge fields to be in the curved spacetime as opposed to an auxiliary flat space. We show how for Gibbons-Hawking spacetimes with more than two centres a generalisation of the Weyl doubling formula is needed by including a derivative-dependent expression which is linear in the Abelian field strength. We also find a type of twisted doubling formula in a case of a manifold with Spin(7) holonomy in eight dimensions. For Einstein Maxwell theories where there is an independent gauge field defined on spacetime, we investigate how the gauge fields determine the Weyl spacetime curvature via a doubling formula. We first show that this occurs for the Reissner-Nordstrom metric in any dimension, and that this generalises to the electrically-charged Born-Infeld solutions. Finally, we consider brane systems in supergravity, showing that a similar doubling formula applies. This Weyl formula is based on the field strength of the p-form potential that minimally couples to the brane and the brane world volume Killing vectors.

中文翻译：

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外尔倍增

我们研究了许多时空，其中外尔曲率可以用阿贝尔场强代数表示。这些包括四维和更高维的 D 型时空，它们遵循场强和外尔张量之间的简单二次关系，遵循外尔自旋量双复制关系。然而，我们通过将规范场置于弯曲时空而不是辅助平坦空间中来偏离通常的双重复制范式。我们展示了对于具有两个以上中心的 Gibbons-Hawking 时空，如何通过包含在阿贝尔场强中呈线性的导数相关表达式来推广 Weyl 倍增公式。我们还在八维具有 Spin(7) 完整度的流形的情况下发现了一种扭曲的加倍公式。对于在时空上定义了独立规范场的爱因斯坦麦克斯韦理论，我们研究规范场如何通过倍增公式确定外尔时空曲率。我们首先表明，这对于任何维度的 Reissner-Nordstrom 度量都会发生，并且这可以推广到带电的 Born-Infeld 解决方案。最后，我们考虑超重力中的膜系统，表明类似的加倍公式适用。该外尔公式基于与膜和膜世界体积杀伤向量最小耦合的 p 型势的场强。并且这推广到带电的 Born-Infeld 解决方案。最后，我们考虑超重力中的膜系统，表明类似的加倍公式适用。该外尔公式基于与膜和膜世界体积杀伤向量最小耦合的 p 型势的场强。并且这推广到带电的 Born-Infeld 解决方案。最后，我们考虑超重力中的膜系统，表明类似的加倍公式适用。该 Weyl 公式基于与膜和膜世界体积杀死矢量最小耦合的 p 型势的场强。