Speed of light on rotating platforms

If is often taken for granted that on a rotating disk it is possible to ope rate a global 3 + 1 splitting of spacetime such that both lengths and time intervals are uniquely defined in terms of measurements performed by real r ods and real clocks at rest on the platform. This paper shows that this ass umption, although widespread and apparently trivial, leads to an anisotropy of the velocity of two light beams traveling in opposite directions along the rim of the disk, which in turn implies some recently pointed out parado xical consequences undermining the self-consistency of rite special theory of relativity (SRT). A correct application of the SRT solves the problem an d recovers complete internal consistency Soi the theory. As an immediate co nsequence, it is shown that the Sagnac effect only depends on the nonhomoge neity of time of the platform and has nothing to do with any anisotropy of the speed of light among the rim of the disk, contrary to an incorrect but widely held idea.