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arXiv 1806.02765gr-qc
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基于洛伦兹群的杨-米尔斯引力理论

Gravity as a Yang-Mills Theory Based on the Lorentz Group

Hans Christian Öttinger

备注：
5 pages, 1 figure
发表信息：
Phys. Rev. Research 2, 013190 (2020)
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摘要：

杨-米尔斯理论与限制洛伦兹群被重新作为一个候选理论的引力。这是一个自然的想法，因为引力和惯性等效原理建议引入具有洛伦兹变换规范自由度的局部惯性坐标系。与以前的实现的想法相比，我们使用的规范理论的矢量势的度量，其中包括一个耦合常数的广义表达式。我们可以证明，在耦合常数很小的情况下，广义相对论的所有经典预言都能重现。对于由此产生的高阶场方程，与黑洞相关的奇点的性质发生了变化。所提出的理论是基于一个无量纲的行动耦合的杨米尔斯场的问题。

英文摘要：

The Yang-Mills theory associated with the restricted Lorentz group is revisited as a candidate for a theory of gravity. This is a natural idea because the principle of equivalence of gravitation and inertia suggests to introduce locally inertial coordinate systems with the gauge freedom of Lorentz transformations. Compared to previous implementations of the idea, we use a generalized expression for the vector potential of the gauge theory in terms of the metric, which involves a coupling constant. One can verify that, in the limit of small coupling constant, all the classical predictions of general relativity are reproduced. For the resulting higher-order field equations, the nature of the singularity associated with black holes changes. The proposed theory is based on a dimensionless action for coupling the Yang-Mills field to matter.

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