Influence of Power-Law Shape Function and Probing Particle Energy on Magnetized Rainbow Wormhole Dynamics

The shape function is a fundamental mathematical tool that governs wormhole geometry, determining its traversability and stability. We investigate the effects of power-law shape function on the occurrence of rainbow traversable wormholes, using magnetic fluid as a source matter. For this purpose, we formed and solved the field equations for dynamical variables. We analyzed these variables for different quantified energy levels of the rainbow probing particles, i.e., E = 0EP (general relativistic case) , 0.1EP , 0.5EP and 0.9EP (EP is Planck's energy), for all three types of rainbow functions. It is evident from the research that for all the four energy levels, the dynamical variables present the same behavior but with different values. The power-law function produces a negative pressure which is the cause of violation of strong energy condition. Thus, the matter source is capable of generating repulsive gravity and potentially driving accelerated expansion of spacetime which indicates the structure stability.