Klein-Gordon particles in a nonuniform external magnetic field in Bonnor-Melvin rainbow gravity background (2504.05717v2)

Abstract: We investigate the effect of rainbow gravity on Klein-Gordon (KG) bosons in a quantized nonuniform magnetic field in the background of Bonnor-Melvin (BM) spacetime with a cosmological constant. In the process, we show that the BM spacetime introduces domain walls (i.e., infinitely impenetrable hard walls) at (r = 0) and (r = \pi/\sqrt{2\Lambda}), as a consequence of the effective gravitational potential field generated by such a magnetized BM spacetime. As a result, the motion of KG particles/antiparticles is restricted indefinitely within the range (r \in [0, \pi/\sqrt{2\Lambda}]), and the particles and antiparticles cannot be found elsewhere. Next, we provide a conditionally exact solution in the form of the general Heun function (H_G(a, q, \alpha, \beta, \gamma, \delta, z)). Within the BM domain walls and under the condition of exact solvability, we study the effects of rainbow gravity on KG bosonic fields in a quantized nonuniform external magnetic field in the BM spacetime background. We use three pairs of rainbow functions: ( f(u) = (1 - \tilde{\beta} |E|)^{-1}, \, h(u) = 1 ); and ( f(u) = 1, \, h(u) = \sqrt{1 - \tilde{\beta} |E|^\upsilon} ), with (\upsilon = 1,2), where (u = |E| / E_p), (\tilde{\beta} = \beta / E_p), and (\beta) is the rainbow parameter. We find that such pairs of rainbow functions, ((f(u), h(u))), fully comply with the theory of rainbow gravity, ensuring that (E_p) is the maximum possible energy for particles and antiparticles alike. Moreover, we show that the corresponding bosonic states form magnetized, rotating vortices, as intriguing consequences of such a magnetized BM spacetime background.