标题： 关于Bonner-Melvin时空中的Klein-Gordon玻色场在彩虹引力中具有宇宙学常数：Bonnor-Melvin域墙 显示英文标题

标题： On the Klein-Gordon bosonic fields in the Bonnor-Melvin spacetime with a cosmological constant in rainbow gravity: Bonnor-Melvin Domain Walls

摘要： 我们研究了彩虹引力对Klein-Gordon (KG)玻色子在带有宇宙常数的磁化Bonnor-Melvin (BM)时空背景下的影响。 首先，我们证明了BM时空度规中正弦项 \(\sin^2(\sqrt{2\Lambda}r)\) 的存在暗示着 \(\sin^2(\sqrt{2\Lambda}r) \in [0,1],\)，这反过来限制了径向坐标 \(r\) 的范围为 \(r \in [0,\pi/\sqrt{2\Lambda}]\)。 此外，我们表明在 \(r = 0\) 和 \(r = \pi/\sqrt{2\Lambda}\) 处，磁化的BM时空引入了域墙（无限不可穿透的硬墙），KG玻色子场可以在其中移动。 有趣的是，磁化的BM时空不仅引入了两个域墙，还引入了一系列域墙。 然而，我们关注的是范围 \(r \in [0,\pi/\sqrt{2\Lambda}]\)。 量子粒子在这个范围内被无限期地限制，不能出现在其他地方。 基于这些发现，我们报告了彩虹引力对BM时空中KG玻色子场的影响。 我们使用三对彩虹函数：\( f(\chi) = \frac{1}{1 - \tilde{\beta} |E|}, \, h(\chi) = 1 \)；\(f(\chi) = (1 - \tilde{\beta} |E|)^{-1}, \, h(\chi) = 1 \)；以及\( f(\chi) = 1, \, h(\chi) = \sqrt{1 - \tilde{\beta} |E|^\upsilon} \)，其中\(\upsilon = 1,2\)。 这里，\(\chi = |E| / E_p\)、\(\tilde{\beta} = \beta / E_p\)和\(\beta\)是彩虹参数。 我们发现，虽然第一和第三种情况中的\((f,h)\)对完全符合彩虹引力理论，并确保\(E_p\)是粒子和反粒子的最大可能能量，但第二种对没有显示出对彩虹引力效应的任何响应。我们还表明，相应的玻色子态可以在单层材料中形成磁化的旋转涡旋，并且这些涡旋可以通过调整外加磁场来驱动。 显示英文摘要

摘要： We investigate the effect of rainbow gravity on Klein-Gordon (KG) bosons in the background of the magnetized Bonnor-Melvin (BM) spacetime with a cosmological constant. We first show that the very existence of the sinusoidal term \(\sin^2(\sqrt{2\Lambda}r)\), in the BM space-time metric, suggests that \(\sin^2(\sqrt{2\Lambda}r) \in [0,1],\) which consequently restricts the range of the radial coordinate \(r\) to \(r \in [0,\pi/\sqrt{2\Lambda}]\). Moreover, we show that at \(r = 0\) and \(r = \pi/\sqrt{2\Lambda}\), the magnetized BM-spacetime introduces domain walls (infinitely impenetrable hard walls) within which the KG bosonic fields are allowed to move. Interestingly, the magnetized BM-spacetime introduces not only two domain walls but a series of domain walls. However, we focus on the range \(r \in [0,\pi/\sqrt{2\Lambda}]\). A quantum particle remains indefinitely confined within this range and cannot be found elsewhere. Based on these findings, we report the effects of rainbow gravity on KG bosonic fields in BM-spacetime. We use three pairs of rainbow functions: \( f(\chi) = \frac{1}{1 - \tilde{\beta} |E|}, \, h(\chi) = 1 \); \( f(\chi) = (1 - \tilde{\beta} |E|)^{-1}, \, h(\chi) = 1 \); and \( f(\chi) = 1, \, h(\chi) = \sqrt{1 - \tilde{\beta} |E|^\upsilon} \), with \(\upsilon = 1,2\). Here, \(\chi = |E| / E_p\), \(\tilde{\beta} = \beta / E_p\), and \(\beta\) is the rainbow parameter. We found that while the pairs \((f,h)\) in the first and third cases fully comply with the theory of rainbow gravity and ensure that \(E_p\) is the maximum possible energy for particles and antiparticles, the second pair does not show any response to the effects of rainbow gravity. We show that the corresponding bosonic states can form magnetized, spinning vortices in monolayer materials, and these vortices can be driven by adjusting an out-of-plane aligned magnetic field.