  We report rigorous calculations of electric dipole moment (EDM) in $^{225}$Ra
due to parity and time-reversal violating tensor-pseudotensor (T-PT) and
nuclear Schiff moment (NSM) interactions between the electrons and nucleus by
employing the relativistic all order coupled-cluster (RCC) methods at various
levels of approximation. The most accurate EDM ($d_A$) results are obtained as
$d_A=-10.04\times 10^{-20} C_T <\sigma_n>|e|cm$ and $d_A^{NSM}=-6.79 \times
10^{-17} S (|e|fm^3)^{-1} |e|cm$ with $C_T$ and $S$ are the T-PT coupling
constant and NSM respectively. Due to exhaustive treatment of the electron
correlation effects in these calculations, the EDM results for the
corresponding T-PT and NSM interactions reduce by about 45\% and 23\%,
respectively, from the previously known values. Nonetheless they are still
found to be 2-3 times larger than the $^{199}$Hg results. Validity of the RCC
results are countenanced by comparing our calculations at the zeroth order
Dirac-Fock method and all order random-phase approximation with the other
groups. In view of the current experimental progress in the $^{225}$Ra EDM
measurement, our high accuracy calculations are very useful to yield limits on
$C_T$ and $S$ in this atom. Thusly, it is possible to realize more accurate
limits on the electron-quark T-PT interaction and $\theta_{QCD}$ parameter of
particle physics in future.
