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 \(r = 0\) E \(r = \pi/\sqrt{2\Lambda}\), 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. Tuttavia, 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: \( f(\chi) = \frac{1}{1 – \tilde{\beta} |E|}, \, h(\chi) = 1 \); \(
f(\chi) = (1 – \tilde{\beta} |E|)^{-1}, \, h(\chi) = 1 \); E \( f(\chi) = 1,
\, h(\chi) = \sqrt{1 – \tilde{\beta} |E|^\upsilon} \), with \(\upsilon = 1,2\).
Here, \(\chi = |E| / E_p\), \(\tilde{\beta} = \beta / E_p\), E \(\beta\) 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. Noi
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.

Questo articolo esplora i giri e le loro implicazioni.

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