Exact solutions and phenomenological constraints from massive scalars in a gravity’s rainbow spacetime

We obtain the exact (confluent Heun) solutions to the massive scalar field in a gravity’s rainbow Schwarzschild metric. With these solutions at hand, we study the Hawking radiation resulting from the tunneling rate through the event horizon. We show that the emission spectrum obeys nonextensive statistics and is halted when a certain mass remnant is reached. Next, we infer constraints on the rainbow parameters from recent LHC particle physics experiments and Hubble STIS astrophysics measurements. Finally, we study the low frequency limit in order to find the modified energy spectrum around the source.

Figure 1

Energy density $\rho (\omega )={\omega }^3{n}_{\omega }$ emitted by a rainbow black hole for growing values of the rainbow parameter, $\xi$, as a function of the frequency. We set $s=2$ and $T=0.1$ in Planck units.