We revisit the static spherically symmetric solutions of Einstein’s general relativity with a conformally coupled scalar field in arbitrary dimensions. Using a four rank tensor introduced earlier we recast the field equations in a manifestly symmetric form to elucidate a somewhat less-known feature of dual mapping between solutions. We also show that there is a two-parameter subfamily of solutions which enjoy a duality symmetry and in four dimensions both the BBMB black hole and the Barcelo–Visser wormhole belong to this subfamily. Along the way, we rederive the full three-parameter family of solutions by direct integration of the field equations and a natural choice of ansatz which arguably has several advantages over other previously known methods.

中文翻译：

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重新审视具有共形耦合标量场的静态球对称重力解


我们重新审视了爱因斯坦广义相对论的静态球对称解，该解具有任意维度的共形耦合标量场。使用前面介绍的四秩张量，我们以明显对称的形式重新转换场方程，以阐明解之间的对偶映射的一个鲜为人知的特征。我们还表明，有一个双参数解亚族，它们享有对偶对称性，在四个维度上，BBMB 黑洞和 Barcelo-Visser 虫洞都属于这个亚族。在此过程中，我们通过直接积分场方程和自然选择的 ansatz 重新推导出完整的三参数解系列，这可以说比其他以前已知的方法具有多个优势。