  We study a three-state (leftist, rightist, centrist) model that couples the
dynamics of social balance with an external deradicalizing field. The
mean-field analysis shows that there exists a critical value of the external
field $p_c$ such that for a weak external field ($p$$<$$p_c$), the system
exhibits a metastable fixed point and a saddle point in addition to a stable
fixed point. However, if the strength of the external field is sufficiently
large ($p$$>$$p_c$), there is only one (stable) fixed point which corresponds
to an all-centrist consensus state (absorbing state). In the weak-field regime,
the convergence time to the absorbing state is evaluated using the
quasi-stationary distribution and is found to be in agreement with the results
obtained by numerical simulations.
