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arXiv 2301.04023gr-qchep-th
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非局域引力中的能量-动量复体

The energy-momentum complex in non-local gravity

Salvatore Capozziello, Maurizio Capriolo, Gaetano Lambiase

AI总结:

本文利用平移不变性和 Noether 定理,将爱因斯坦引力能量-动量赝张量推广到含 $\Box^{-1}$ 解析函数的非局域引力,并证明其局域守恒及弱场形式。

摘要:

在广义相对论中,定义给定空间区域内所含引力能量的问题仍未解决,只有在特定时空满足渐近平坦性的局域化物体等特殊情形下例外。原则上,如果某一特定体积内的总能量含量不能被唯一界定,那么一种引力理论就不是自洽的。在本文中,我们将爱因斯坦引力能量-动量赝张量推广到非局域引力理论,其中考虑了非局域积分算子 $\Box^{-1}$ 的解析函数。我们将 Noether 定理应用于引力拉格朗日量,并假定其在单参数微分同胚群(即无穷小刚体平移)下保持不变。非局域引力作用量在整体平移下的不变性会产生一个局域守恒的 Noether 流,从而给出引力能量-动量赝张量的定义;该赝张量是一个仿射对象,在仿射变换下像张量一样变换。此外,得益于非局域缩并 Bianchi 恒等式,能量-动量复体仍保持局域守恒。由此可以推导引力赝张量以及同时计入引力和物质分量的能量-动量复体的连续性方程。最后,鉴于天体物理应用,我们在度规扰动的最低阶上计算了赝张量的弱场极限。

英文摘要:

In General Relativity, the issue of defining the gravitational energy contained in a given spatial region is still unresolved, except for particular cases of localized objects where the asymptotic flatness holds for a given spacetime. In principle, a theory of gravity is not self-consistent, if the whole energy content is not uniquely defined in a specific volume. Here we generalize the Einstein gravitational energy-momentum pseudotensor to non-local theories of gravity where analytic functions of the non-local integral operator $\Box^{-1}$ are taken into account. We apply the Noether theorem to a gravitational Lagrangian, supposed invariant under the one-parameter group of diffeomorphisms, that is, the infinitesimal rigid translations. The invariance of non-local gravitational action under global translations leads to a locally conserved Noether current, and thus, to the definition of a gravitational energy-momentum pseudotensor, which is an affine object transforming like a tensor under affine transformations. Furthermore, the energy-momentum complex remains locally conserved, thanks to the non-local contracted Bianchi identities. The continuity equations for the gravitational pseudotensor and the energy-momentum complex, taking into account both gravitational and matter components, can be derived. Finally, the weak field limit of pseudotensor is performed to lowest order in metric perturbation in view of astrophysical applications.

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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