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arXiv 2302.02685hep-thgr-qcquant-ph
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德西特时空中宇宙弦诱导的电磁真空应力与能流

Electromagnetic vacuum stresses and energy fluxes induced by a cosmic string in de Sitter spacetime

A. A. Saharian, V. F. Manukyan, V. Kh. Kotanjyan, A. A. Grigoryan

AI总结:

该研究分析了(D+1)维德西特时空中广义宇宙弦缺陷对电磁场Bunch-Davies真空能量-动量张量的影响,明确了拓扑贡献的分布、能流特性及不同距离下的衰减规律。

摘要:

针对(D+1)维局域德西特(dS)时空中的电磁场,我们分析了广义宇宙弦型缺陷对能量-动量张量真空期望值的影响。对于Bunch-Davies真空态,我们明确提取了对角分量与非对角分量中的拓扑贡献。非对角分量表征了真空态中径向能流的存在:由于电磁场的共形不变性,该能流在D=3时为零;在D≥4时,能流方向指向宇宙弦。真空应力中的拓扑贡献具有各向异性,与闵可夫斯基时空中的宇宙弦几何不同,当D>3时,平行于弦核方向的应力与能量密度不相等。根据平面角亏缺和与宇宙弦的距离不同,对应的期望值既可以为正,也可以为负。在靠近宇宙弦的区域,引力场对拓扑部分对角分量的影响较弱。当时空点与宇宙弦的固有距离大于dS曲率半径时,时空曲率会显著改变拓扑项的行为。在该区域内,对于所有空间维度D的取值,能量-动量张量对角分量的拓扑贡献均以固有距离的四次方反比衰减,能流密度则以五次方反比衰减;唯一的例外是D=4这一特殊情形下的能量密度。

英文摘要:

For the electromagnetic field in (D+1)-dimensional locally de Sitter (dS) spacetime, we analyze the effects of a generalized cosmic string type defect on the vacuum expectation value of the energy-momentum tensor. For the Bunch-Davies vacuum state, the topological contributions are explicitly extracted in both the diagonal and off-diagonal components. The latter describes the presence of radially directed energy flux in the vacuum state. It vanishes for $D=3$ because of the conformal invariance of the electromagnetic field and is directed towards the cosmic string for $D\geq 4$ . The topological contributions in the vacuum stresses are anisotropic and, unlike to the geometry of a cosmic string in the Minkowski spacetime, for $D>3$ the stresses along the directions parallel to the string core differ from the energy density. Depending on the planar angle deficit and the distance from the cosmic string, the corresponding expectation values can be either positive or negative. Near the cosmic string the effect of the gravitational field on the diagonal components of the topological part is weak. The spacetime curvature essentially modifies the behavior of the topological terms at proper distances from the cosmic string larger than the dS curvature radius. In that region, the topological contributions in the diagonal components of the energy-momentum tensor decay in inverse proportion to the fourth power of the proper distance and the energy flux density behaves as inverse-fifth power for all values of the spatial dimension $D$. The exception is the energy density in the special case $D=4$.

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