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In this paper we study black string solutions under the consideration ofrainbow gravity. We have analytically obtained the solution forfour-dimensional black strings in terms of the functions $f(E/E_p)$ and$g(E/E_p)$ that sets the energy scale where the rainbow gravity becomesrelevant. We have also obtained the Hawking temperature for the black string,from which we could see that the rainbow functions play the role of increasingor decreasing the Hawking temperature for a given horizon radius depending onthe choice of such rainbow functions. We have computed the entropy, specificheat and free energy for the black string. The entropy and specific heatexhibit a rainbow dependence, while the free energy is not modified by therainbow functions. Finally we have studied the effects of the rainbow gravityin the orbits of massive and massless particles around a black string. We couldverify that neither massive nor massless particles exhibit stable orbits arounda black string in the scenario of rainbow gravity, for any configuration ofrainbow functions.

Black String solutions in Rainbow Gravity