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arXiv 0905.3622gr-qc
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Einstein-Gauss-Bonnet引力扰动的三种超势

Three types of superpotentials for perturbations in the Einstein-Gauss-Bonnet gravity

A. N. Petrov

摘要:

构造了任意弯曲背景上任意扰动下的爱因斯坦-高斯-博内(EGB)引力超势(反对称张量密度)。作为基础,广义守恒律的框架内的任意D维度量理论,其中保守的电流表示通过发散的超势,被使用。这样的推导是精确的(扰动不是无穷小的),并且当一个解(动力学)被认为是相对于另一个解(背景)的扰动系统时,可以接近。三个已知的处方详细说明:这些是典型的Nether定理,Belinfante对称化规则和场论推导。所有这三种方法都以一种独特的方式提出,便于比较和发展。当EGB引力中的任意静态Schwarzschild类解被认为是关于同一类型背景的扰动系统时,导出了三种类型超势的01分量的精确表达式.这些公式被用来计算EGB引力下Schwarzschild-anti-de Sitter黑洞的质量。作为背景,考虑任意维的反德西特时空和5维的非最大对称“质量隙”真空。问题和未来的发展前景,包括洛夫洛克重力,进行了讨论。

英文摘要:

Superpotentials (antisymmetric tensor densities) in Einstein-Gauss-Bonnet (EGB) gravity for arbitrary types of perturbations on arbitrary curved backgrounds are constructed. As a basis, the generalized conservation laws in the framework of an arbitrary D-dimensional metric theory, where conserved currents are expressed through divergences of superpotentials, are used. Such a derivation is exact (perturbations are not infinitesimal) and is approached, when a one solution (dynamical) is considered as a perturbed system with respect to another solution (background). Three known prescriptions are elaborated: these are the canonical Nœther theorem, the Belinfante symmetrization rule and the field-theoretical derivation. All the three approaches are presented in an unique way convenient for comparisons and a development. Exact expressions for the 01-component of the three types of the superpotentials are derived in the case, when an arbitrary static Schwarzschild-like solution in the EGB gravity is considered as a perturbed system with respect to a background of the same type. These formulae are used for calculating the mass of the Schwarzschild-anti-de Sitter black hole in the EGB gravity. As a background both the anti-de Sitter spacetime in arbitrary dimensions and a not maximally symmetric "mass gap" vacuum in 5 dimensions are considered. Problems and perspectives for a future development, including the Lovelock gravity, are discussed.

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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