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In this paper we treat the so called clock paradox in an analytical way byassuming that a constant and uniform force F of finite magnitude actscontinuously on the moving clock along the direction of its motion assumed tobe rectilinear. No inertial motion steps are considered. The rest clock isdenoted as (1), the to-and-fro moving clock is (2), the inertial frame in which(1) is at rest in its origin and (2) is seen moving is I and, finally, theaccelerated frame in which (2) is at rest in its origin and (1) moves forwardand backward is A. We deal with the following questions: I) What is the effectof the finite force acting on (2) on the proper time intervals measured by thetwo clocks when they reunite? Does a differential aging between the two clocksoccur, as it happens when inertial motion and infinite values of theaccelerating force is considered? The Special Theory of Relativity is used inorder to describe the hyperbolic motion of (2) in the frame I II) Is thiseffect an absolute one, i.e. does the accelerated observer A comoving with (2)obtain the same results as that in I, both qualitatively and quantitatively, asit is expected? We use the General Theory of Relativity in order to answer thisquestion.Comment: LaTex2e, 19 pages, no tables, no figures. Rewritten version, it  amends the previous one whose results about the treatment with General  Relativity were wrong. References added. Eq. (55) corrected. More refined  version. Comments and suggestions are warmly welcom

An Analytical Treatment of the Clock Paradox in the Framework of the Special and General Theories of Relativity