http://arxiv.org/abs/2304.06546
We argue that, as long as relativistic quantum particles are in point, the variable $y=E/E_p$ of the rainbow functions pair $g_{{0}} (y)$ and $g{{1}} (y)$ should be fine tuned into $y=|E|/E_p$, where $E_p$ is the Planck’s energy scale. Otherwise, the rainbow functions will be only successful to describe the rainbow gravity effect on relativistic quantum particles and the anti-particles will be left unfortunate. Under such fine tuning, we consider Klein-Gordon (KG) particles in cosmic string rainbow gravity spacetime in a non-uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{3}{2}B{\circ }r\,\hat{z}$ ). Then we consider KG-particles in cosmic string rainbow gravity spacetime in a uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times \mathbf{A}=\frac{1}{2}B_{\circ }\,\hat{z}$ ). Whilst the former effectively yields KG-oscillators, the later effectively yields KG-Coulombic particles. We report on the effects of rainbow gravity on both KG-oscillators and Coulombic particles using four pairs of rainbow functions: (i) $% g_{{0}}\left( y\right) =1$, $g{{1}}\left( y\right) =\sqrt{1-\epsilon y^{2}% }$, (ii) $g{{0}}\left( y\right) =1$, $g{{1}}\left( y\right) =\sqrt{% 1-\epsilon y}$, (iii) $g{{0}}\left( y\right) =g{{1}}\left( y\right) =\left( 1-\epsilon y\right) ^{-1}$, and (iv) $g{{0}}\left( y\right) =\left( e^{\epsilon y}-1\right) /\epsilon y$, $g{_{1}}\left( y\right) =1$, where $y=|E|/E_p$ and $\epsilon$ is the rainbow parameter. It is interesting to report that, all KG particles’ and anti-particles’ energies are symmetric about $E=0$ value (a natural relativistic quantum mechanical tendency), and a phenomenon of energy states to fly away and disappear from the spectrum is observed for the rainbow functions pair (iii) at $\gamma=\epsilon m/E_p=1$.
O. Mustafa
Fri, 14 Apr 23
46/64
Comments: 15 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:2301.05464, arXiv:2301.12370
You must be logged in to post a comment.