Abstract A Review on attempts to propose alternative theories to the General Relativity is presented. The restriction is on classical models/theories and comprise rather algebraic extensions of the theory of General Relativity. First, possible algebraic extensions of the space–time coordinates and metric extensions are presented, with a discussion of their problems and limits. The pseudo-complex General Relativity, an algebraic extension, will show definite predictions and is compared to observations. A particular description of General Relativity, using the canonical transformation formalism, is shown to have new solutions through the generalization of the Einstein equations and providing a satisfying description of the acceleration of the universe. Finally, the MOND model with its predictions and the Quintessence are briefly explained, including their relations to the formerly exposed extensions of General Relativity. Attempts to quantize the theory (String Theory or Loop Quantum Gravity) will be mentioned only briefly.

中文翻译：

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爱因斯坦广义相对论的替代方案

摘要 对提出广义相对论替代理论的尝试进行了回顾。限制是对经典模型/理论，包括广义相对论的代数扩展。首先，提出了时空坐标的可能代数扩展和度量扩展，并讨论了它们的问题和限制。伪复杂广义相对论是代数扩展，将显示明确的预测并与观察进行比较。广义相对论的一个特殊描述，使用正则变换形式主义，被证明通过爱因斯坦方程的推广有新的解决方案，并提供了对宇宙加速度的令人满意的描述。最后，简要说明MOND模型及其预测和Quintessence，包括它们与以前公开的广义相对论扩展的关系。将仅简要提及量化理论（弦理论或圈量子引力）的尝试。