GR和其它度量理论中弯曲背景下的非线性扰动和守恒律
Nonlinear Perturbations and Conservation Laws on Curved Backgrounds in GR and Other Metric Theories
摘要：
场论方法进行了审查。在广义相对论以及任意$D$维度规理论中的微扰都是在理论的解（任意）的背景下研究的。定义了微扰的拉格朗日量，并由变分原理导出了微扰的场方程。这些方程是精确的，等价于标准公式中的方程，但也可以是近似的。场论描述在规范（内部）变换下是不变的，可以用精确和近似的形式表示。遵循通常的场论处方，构造了微扰的守恒量。守恒电流通过超势的发散--反对称张量密度来表示。这种形式允许相关的必要性，以考虑局部性质的扰动与理论表示准本地性质的保守量在度量理论。讨论了该形式在广义相对论中的应用。在Einstein-Gauss-Bonnet引力中检验了任意度量$D$维理论的推广公式。
英文摘要：
The field-theoretical approach is reviewed. Perturbations in general relativity as well as in an arbitrary $D$-dimensional metric theory are studied on a background, which is a solution (arbitrary) of the theory. Lagrangian for perturbations is defined, and field equations for perturbations are derived from the variational principle. These equations are exact and equivalent to the equations in the standard formulation, but can be approximate also. The field-theoretical description is invariant under gauge (inner) transformations, which can be presented both in exact and approximate forms. Following the usual field-theoretical prescription, conserved quantities for perturbations are constructed. Conserved currents are expressed through divergences of superpotentials -- antisymmetric tensor densities. This form allows to relate a necessity to consider local properties of perturbations with a theoretical representation of the quasi-local nature of conserved quantities in metric theories. Applications of the formalism in general relativity are discussed. Generalized formulae for an arbitrary metric $D$-dimensional theory are tested in the Einstein-Gauss-Bonnet gravity.
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