Derives a general expression for the temporal growth rate of synchrotron waves being excited as a result of the interaction between a general relativistic plasma and an ambient cold magnetoactive plasma. This expression is shown to be composed of two terms, one pertaining to waves of polarization 1 and the other for waves of polarization 2. Analytical expressions for the temporal growth rate as well as spacial amplification rate for wave 2 are obtained for the case when the relativistic plasma forms a nearly monoenergetic helical stream.