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The possible transverse polarization of the $\tau$-lepton, which is $T$-oddand can be used to measure CP-violation, is estimated precisely in theradiative decay mode $B_c \to \tau \bar \nu_\tau \gamma$ with possibleparameters for the multi Higgs doublet model and the R-parity violatingsupersymmetric model. We find that the up-bound of the transverse polarizationwith possible parameters in the models is at very different levels i.e. it canbe $\leq 15\sim 23%$ for the former but $\leq 0.1 %$ for the latter, and it isaccessible experimentally soon.Comment: 14 pages, latex, 3 figures, appear in J. Phys.

Transverse $\tau$ polarization in Bc $\rightarrow$ $\tau$$\bar nu$$\tau$$\gamma$ decay