引力的$4$指数理论及其与能量-动量守恒定律破坏的关系
$4$-index theory of gravity and its relation with the violation of the energy-momentum conservation law
摘要：
最近，Moulin（Eur.）提出了爱因斯坦理论的$4$指数推广。J. C 77，878（2017））。利用这种方法，我们找到了最一般的$2$ -指数场方程可导出的Einstein-Hilbert作用。研究了牛顿极限的应用、引力耦合常数的作用以及能量动量张量性质对建立$4$指数引力理论的影响。我们还讨论了建立Weyl自由$4$指数引力理论的结果。我们的研究表明，Einstein理论和Rastall理论都可以作为$4$ -指数引力理论的子类得到，这表明了$4$ -指数方法在统一各种引力理论方面的作用。本文还证明了在$4$ -指数引力理论中，能量-动量守恒定律的破坏是可以允许的，而且$4$ -指数引力理论的收缩一般允许几何与物质场之间存在Rastall方式的非最小耦合。这项研究还表明，不同于爱因斯坦的情况下，引力耦合常数的$4$指数Rastall理论一般不同于普通的$2$指数Rastall理论。
英文摘要：
Recently, a $4$-index generalization of the Einstein theory is proposed by Moulin (Eur. Phys. J. C 77, 878 (2017)). Using this method, we find the most general $2$-index field equations derivable from the Einstein-Hilbert action. The application of Newtonian limit, the role of gravitational coupling constant and the effects of the properties of ordinary energy-momentum tensor in obtaining a $4$-index gravity theory have been studied. We also address the results of building Weyl free $4$-index gravity theory. Our study displays that both the Einstein and Rastall theories can be obtained as the subclasses of a $4$-index gravity theory which shows the power of $4$-index method in unifying various gravitational theories. It is also obtained that the violation of the energy-momentum conservation law may be allowed in $4$-index gravity theory, and moreover, the contraction of $4$-index theory generally admits a non-minimal coupling between geometry and matter field in the Rastall way. This study also shows that, unlike the Einstein case, the gravitational coupling constant of $4$-index Rastall theory generally differs from that of the ordinary $2$-index Rastall theory.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
