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The determination of the electromagnetic field generated by a charge inhyperbolic motion is a classical problem for which the majority view is thatthe Li\'enard-Wiechert solution which implies that the charge radiates) is thecorrect one. However we analyze in this paper a less known solution due toTurakulov that differs from the Li\'enard-Wiechert one and which according tohim does not radiate. We prove his conclusion to be wrong. We analyze theimplications of both solutions concerning the validity of the EquivalencePrinciple. We analyze also two other issues related to hyperbolic motion, theso-called Bell's "paradox" which is as yet source of misunderstandings and theUnruh effect, which according to its standard derivation in the majority of thetexts, is a correct prediction of quantum field theory. We recall that thestandard derivation of the Unruh effect does not resist any tentative of anyrigorous mathematical investigation, in particular the one based in thealgebraic approach to field theory which we also recall. These results make usto align with some researchers that also conclude that the Unruh effect doesnot exist.

Life in the Rindler Reference Frame: Does an Uniformly Accelerated Charge Radiates? Is there a Bell `Paradox'? Is Unruh Effect Real?