In this manuscript, we show that the external Schwarzschild metric can be a good approximation of exact black hole solutions of entangled relativity. Since entangled relativity cannot be defined from vacuum, the demonstrations need to rely on the definition of matter fields. The electromagnetic field being the easiest (and perhaps the only) existing matter field with infinite range to consider, we study the case of a charged black hole – for which the solution of entangled relativity and a dilaton theory agree – as well as the case of a pure radiation – for which the solution of entangled relativity and general relativity seem to agree, despite an apparent ambiguity in the field equations. Based on these results, we argue that the external Schwarzschild metric is an appropriate mathematical idealization of a spherical black hole in entangled relativity. The extension to rotating cases is briefly discussed.

在这份手稿中，我们表明外部施瓦西度量可以很好地近似纠缠相对论的精确黑洞解。由于纠缠相对论不能从真空中定义，演示需要依赖于物质场的定义。电磁场是最简单的（也许是唯一的）具有无限范围的现有物质场，我们研究了带电黑洞的情况——纠缠相对论的解和膨胀理论一致——以及纯辐射——纠缠相对论和广义相对论的解似乎一致，尽管场方程中存在明显的歧义。基于这些结果，我们认为外部 Schwarzschild 度量是纠缠相对论中球形黑洞的适当数学理想化。简要讨论了轮换案件的扩展。