arXiv 2011.105032020-11gr-qcastro-ph.CO

作为$f(R,\mathcal{L}_m)$和$f(R,T)$理论的Rastall引力公式

On Rastall gravity formulation as a $f(R,\mathcal{L}_m)$ and a $f(R,T)$ theory

Júlio C. Fabris, Oliver F. Piattella, Davi C. Rodrigues

备注：: 11 pages, accepted for publication in the European Physical Journal Plus

摘要：

拉斯特尔引入了一个应力-能量张量，其发散度与里奇标量的梯度成正比。这个提议导致了广义相对论场方程形式的改变，但它保留了自由度的数量。Rastall的场方程可以被解释为具有重新定义的SET的GR，或者它可以在物质扇区内暗示不同的物理后果。我们调查的限制下，Rastall场方程可以直接从一个行动，特别是从两个$f(R)$ -重力扩展：$f(R,\mathcal L_m)$和$f(R,T)$。我们表明，这些理论之间有相似之处，但Rastall集不能完全恢复，除了某些特殊情况下，这里讨论。值得注意的是，一个简单的，协变的和可逆的重新定义的SET，如Rastall提出的，是很难直接实施的行动。

英文摘要：

Rastall introduced a stress-energy tensor whose divergence is proportional to the gradient of the Ricci scalar. This proposal leads to a change in the form of the field equations of General Relativity, but it preserves the number of degrees of freedom. Rastall's field equations can be either interpreted as GR with a redefined SET, or it can imply different physical consequences inside the matter sector. We investigate limits under which the Rastall field equations can be directly derived from an action, in particular from two $f(R)$-gravity extensions: $f(R,\mathcal L_m)$ and $f(R,T)$. We show that there are similarities between these theories, but the Rastall SET cannot be fully recovered from them, apart from certain particular cases here discussed. It is remarkable that a simple, covariant and invertible redefinition of the SET, as the one proposed by Rastall, is hard to be directly implemented in the action.

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。

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英文摘要：

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