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arXiv 1008.4061gr-qcastro-ph.CO
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线引力的能量和动量局域化

Localizing the Energy and Momentum of Linear Gravity

Luke M. Butcher, Michael Hobson, Anthony Lasenby

摘要:

一个框架的发展,量化的物质和线性化的引力场之间的能量和动量的本地交换。我们导出了与这种描述相一致的唯一的引力能量动量张量,并发现这种张量只存在于谐振规范中。因此,我们框架中几乎所有的规范自由度都被自然地、可替换地移除了。引力能动量张量具有两个特殊的性质:(a)对于引力平面波,它是规范不变的;(b)对于任意的横截无迹场,能量密度永远不是负的,能流永远不是类空的。本文详细分析了引力场与无穷小点源之间的定域规范不变能量动量转移,指出这些不变量只依赖于场的横观无迹分量。结果,我们被引导到一个自然的规范固定程序,它最终使线性引力场的能量-动量完全明确,并且还确保引力能永远不是负的,也不会比光快。最后,我们计算了引力平面波、线性化史瓦西时空(扩展到任意静态线性时空)和两个紧致源(振动棒和等质量双星)外的引力辐射的能量动量含量。

英文摘要:

A framework is developed which quantifies the local exchange of energy and momentum between matter and the linearized gravitational field. We derive the unique gravitational energy-momentum tensor consistent with this description, and find that this tensor only exists in the harmonic gauge. Consequently, nearly all the gauge freedom of our framework is naturally and unavoidably removed. The gravitational energy-momentum tensor is then shown to have two exceptional properties: (a) it is gauge-invariant for gravitational plane-waves, (b) for arbitrary transverse-traceless fields, the energy-density is never negative, and the energy-flux is never spacelike. We analyse in detail the local gauge invariant energy-momentum transferred between the gravitational field and an infinitesimal point-source, and show that these invariants depend only on the transverse-traceless components of the field. As a result, we are led to a natural gauge-fixing program which at last renders the energy-momentum of the linear gravitational field completely unambiguous, and additionally ensures that gravitational energy is never negative nor flows faster than light. Finally, we calculate the energy-momentum content of gravitational plane-waves, the linearized Schwarzschild spacetime (extending to arbitrary static linear spacetimes) and the gravitational radiation outside two compact sources: a vibrating rod, and an equal-mass binary.

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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