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arXiv 1003.1617gr-qc
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引力理论普适性定理的新例

New Cases of Universality Theorem for Gravitational Theories

L. Fatibene, M. Ferraris, M. Francaviglia

摘要:

引力的“普适性定理”表明,真空中的f(R)理论(在它们的度规仿射表述中)在动力学上等价于具有适当宇宙学常数的真空爱因斯坦方程。这对一般的解析函数f(R)(即除了零星的简并情况)也是成立的,如果f是恒等函数(即f(R)=R),则没有宇宙学常数的标准引力也可以重现。定理在这里扩展引入在4维1参数家庭的不变量R'的灵感来自Barbero-Immirzi制定的GR(在欧几里德部门也包括自对偶制定)。将证明这样定义的f(R ')理论与相应的度量仿射f(R)理论是动态等价的。特别是对于函数f(R)=R,得到了GR与Holst拉格朗日量的标准等价性。

英文摘要:

The "Universality Theorem" for gravity shows that f(R) theories (in their metric-affine formulation) in vacuum are dynamically equivalent to vacuum Einstein equations with suitable cosmological constants. This holds true for a generic (i.e. except sporadic degenerate cases) analytic function f(R) and standard gravity without cosmological constant is reproduced if f is the identity function (i.e. f(R)=R). The theorem is here extended introducing in dimension 4 a 1-parameter family of invariants R' inspired by the Barbero-Immirzi formulation of GR (which in the Euclidean sector includes also selfdual formulation). It will be proven that f(R') theories so defined are dynamically equivalent to the corresponding metric-affine f(R) theory. In particular for the function f(R)=R the standard equivalence between GR and Holst Lagrangian is obtained.

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