An Exact Invariant for Relativistic Linear Harmonic Oscillator with Time-dependent Frequency

In this paper we give an exact invariant for a relativistic linear harmonic oscillator with time-dependent frequency. This is accomplished, following Eliezer and Gray , for the non-relativistic case, by associating a relativistic plane isotropic harmonic oscillator with this problem. This exact invariant reflects the conservation of angular momentum of the associated relativistic plane isotropic oscillator. Departures in the physical interpretations of this exact invariant caused by relativistic effects are pointed out.