A brief review on algebraic extensions of general relativity is presented. After a short summary of first attempts by Max Born and Albert Einstein, all possible algebraic extensions will be discussed, with the pseudo-complex (pc) extension left as the only viable one, because it does not contain ghost solutions. Also some metric extensions are presented, such as the non-symmetric gravitation theory and the Finsler metric. Some predictions of the pc extension are discussed, such as the structure of light emission of an accretion disk around a black hole, the redshift at the surface of a compact star as a function in the azimuthal angle, and whether there is an upper limit for the mass of a neutron star.

中文翻译：

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广义相对论中的代数扩展综述

简要回顾了广义相对论的代数扩展。在对 Max Born 和 Albert Einstein 的首次尝试进行简短总结后，将讨论所有可能的代数扩展，而伪复数 (pc) 扩展将作为唯一可行的扩展，因为它不包含幻影解。还介绍了一些度量扩展，例如非对称引力理论和芬斯勒度量。讨论了对 pc 扩展的一些预测，例如黑洞周围吸积盘的发光结构、致密星表面的红移作为方位角的函数，以及是否有上限中子星的质量。