English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We argue that, as long as relativistic quantum particles are in point, thevariable $y=E/E_p$ 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 energyscale. Otherwise, the rainbow functions will be only successful to describe therainbow gravity effect on relativistic quantum particles and the anti-particleswill be left unfortunate. Under such fine tuning, we consider Klein-Gordon (KG)particles in cosmic string rainbow gravity spacetime in a non-uniform magneticfield (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 gravityspacetime in a uniform magnetic field (i.e., $\mathbf{B}=\mathbf{\nabla }\times\mathbf{A}=\frac{1}{2}B_{\circ }\,\hat{z}$ ). Whilst the former effectivelyyields KG-oscillators, the later effectively yields KG-Coulombic particles. Wereport on the effects of rainbow gravity on both KG-oscillators and Coulombicparticles 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 $\epsilon$ isthe rainbow parameter. It is interesting to report that, all KG particles' andanti-particles' energies are symmetric about $E=0$ value (a naturalrelativistic quantum mechanical tendency), and a phenomenon of energy states tofly away and disappear from the spectrum is observed for the rainbow functionspair (iii) at $\gamma=\epsilon m/E_p=1$.

Fine tuning of rainbow gravity functions and Klein-Gordon particles in cosmic string rainbow gravity spacetime