  We present the double real radiation contributions to the $t \bar t$ hadronic
production cross section stemming from the partonic process $gg\rightarrow
t\bar{t}q\bar{q}$. We explicitly construct the antenna subtraction terms for
this gluon-gluon initiated process starting from the double soft behaviour of
the double real radiation matrix elements using soft currents. Those
subtraction terms, given in leading and subleading colour contributions,
require the use of new genuine NNLO four-parton antenna functions involving
massive fermions. Those are also presented together with their infrared limits
in this paper. We checked the validity of our subtraction terms numerically by
showing that the ratio between the real radiation matrix elements and the
subtraction terms approaches unity in all single and double unresolved regions
of phase space.
