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arXiv 0906.0926gr-qcastro-ph.CO
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自举引力:能量-动量自耦合的一致方法

Bootstrapping gravity: a consistent approach to energy-momentum self-coupling

Luke M. Butcher, Michael Hobson, Anthony Lasenby

摘要:

一般认为,引力子(一种经典的无质量自旋为2的场)与其自身的能量-动量张量耦合成功地逐阶重建了爱因斯坦场方程的动力学;然而,这一想法的有效性最近受到了质疑[1]。受此启发,我们提出了一个引力子作用量,其能量-动量自耦合确实符合爱因斯坦场方程。这个引力子的希尔伯特能量-动量张量被明确地计算出来,并被证明提供了场方程中正确的二阶项;相反,菲兹-泡利作用量不能提供正确的项。然后发展了基于度规的引力理论的微扰展开的形式主义,并采用这些技术来证明我们的引力子作用是一个简单的能量-动量自耦合过程的起点,该过程逐阶产生爱因斯坦-希尔伯特作用(直到经典无关的表面项)。将微扰形式扩展到包含物质和宇宙学常数,研究了真空背景下自由物质场和引力场的微扰相互作用.最后,研究了非真空背景的影响,发现引力子在作用中产生了一个非零的“质量项”。

英文摘要:

It is generally believed that coupling the graviton (a classical Fierz-Pauli massless spin-2 field) to its own energy-momentum tensor successfully recreates the dynamics of the Einstein field equations order by order; however the validity of this idea has recently been brought into doubt [1]. Motivated by this, we present a graviton action for which energy-momentum self-coupling is indeed consistent with the Einstein field equations. The Hilbert energy-momentum tensor for this graviton is calculated explicitly and shown to supply the correct second-order term in the field equations; in contrast, the Fierz-Pauli action fails to supply the correct term. A formalism for perturbative expansions of metric-based gravitational theories is then developed, and these techniques employed to demonstrate that our graviton action is a starting point for a straightforward energy-momentum self-coupling procedure that, order by order, generates the Einstein-Hilbert action (up to a classically irrelevant surface term). The perturbative formalism is extended to include matter and a cosmological constant, and interactions between perturbations of a free matter field and the gravitational field are studied in a vacuum background. Finally, the effect of a non-vacuum background is examined, and the graviton is found to develop a non-vanishing ``mass-term'' in the action.

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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