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arXiv 2210.16397gr-qchep-th
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红外效应与 Unruh 态

Infrared Effects and the Unruh State

Paul R. Anderson, Shohreh Gholizadeh Siahmazgi, Zachary P. Scofield

AI总结:

本文研究二维永恒黑洞 Unruh 态中标量场模式的晚时红外行为,证明有效势的散射可消除归一化导致的红外发散及两点函数中的线性时间增长项。

摘要:

本文研究了二维各种永恒黑洞中 Unruh 态下量子化标量场模式的详细行为。结果表明,量子场的某些模式以及对称两点函数的晚时行为由红外效应决定。这些效应的性质取决于模式方程中是否存在有效势,以及该势采取何种形式。文中考虑了三种情形:一种没有势,另外两种势在各处均非负,并且在黑洞事件视界上为零,同时在无穷远或宇宙学视界处为零。具体而言,这些势包括 δ 函数势,以及出现在 Schwarzschild-de Sitter 时空中有质量标量场的势。在这两种情况下,散射效应消除了模式函数中原本会由归一化过程产生的红外发散。当此类红外发散被消除后发现,在过去黑洞视界上相对于 Kruskal 时间为正频率的模式,在径向坐标保持固定而时间坐标趋于无穷大的极限下趋于零。相比之下,当不存在势并因此出现红外发散时,同样的模式在径向坐标保持固定的晚时极限下趋于非零常数。对于二维某些渐近平坦黑洞时空中的 δ 函数势情形,本文研究了场处于 Unruh 态时对称两点函数的行为。模式函数中红外发散的消除,导致随时间线性增长的项被消除。

英文摘要:

Detailed behaviors of the modes of quantized scalar fields in the Unruh state for various eternal black holes in two dimensions are investigated. It is shown that the late-time behaviors of some of the modes of the quantum fields and of the symmetric two-point function are determined by infrared effects. The nature of these effects depends upon whether there is an effective potential in the mode equation and what form this potential takes. Here, three cases are considered, one with no potential and two with potentials that are nonnegative everywhere and are zero on the event horizon of the black hole and zero at either infinity or the cosmological horizon. Specifically, the potentials are a delta function potential and the potential that occurs for a massive scalar field in Schwarzschild-de Sitter spacetime. In both cases, scattering effects remove infrared divergences in the mode functions that would otherwise arise from the normalization process. When such infrared divergences are removed, it is found that the modes that are positive frequency with respect to the Kruskal time on the past black hole horizon approach zero in the limit that the radial coordinate is fixed and the time coordinate goes to infinity. In contrast, when there is no potential and thus infrared divergences occur, the same modes approach nonzero constant values in the late-time limit when the radial coordinate is held fixed. The behavior of the symmetric two-point function when the field is in the Unruh state is investigated for the case of a delta function potential in certain asymptotically flat black hole spacetimes in two dimensions. The removal of the infrared divergences in the mode functions results in the elimination of terms that grow linearly in time.

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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