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Three self-gravitating $SO(10)$ domain walls in five dimensions are obtainedand their properties are analyzed. These non-abelian domain walls interpolatebetween AdS${}_5$ spacetimes with different embedding of $SU(5)$ in $SO(10)$and they can be distinguished, among other features, by the unbroken group oneach wall, being either $SO(10)$, $SO(6)\otimes SU(2)\otimes U(1)/Z_2$ or$SU(4)\otimes SO(2)\otimes U(1)/Z_4$. We show that, unlike Minkowskianversions, the curved scenarios are perturbatively stable due to thegravitational capture of scalar fluctuations associated to the residualorthogonal subgroup in the core of the walls. These stabilizer modes areadditional to the four-dimensional Nambu-Goldstone states found in two of thethree gravitational sceanarios.

$SO(10)$ thick branes and perturbative stability