Klein-Gordon Particles in a Nonuniform External Magnetic Field in Bonnor-Melvin Rainbow Gravity Background

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 root impenetrable hard walls) at r = 0 and r = pi/root 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 parti root cles/antiparticles is restricted indefinitely within the range r is an element of [0, pi/root 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 - (beta) over tilde vertical bar E vertical bar)(-1) , h(u) = 1; anf f(u) = root 1 - (beta) over tilde vertical bar E vertical bar(u), with v = 1, 2, where u = vertical bar E vertical bar/E-p, (beta) over tilde = 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.