  We find a two-parameter family of solutions of the Yang-Mills equations for
gauge group SO(1,3) on Minkowski space by foliating different parts of it with
non-compact coset spaces with SO(1,3) isometry. The interior of the lightcone
is foliated with hyperbolic space $H^3\cong \text{SO}(1,3)/\text{SO}(3)$, while
the exterior of the lightcone employs de Sitter space dS$_3\cong
\text{SO}(1,3)/\text{SO}(1,2)$. The lightcone itself is parametrized by
SO(1,3)/ISO(2) in a nilpotent fashion. Equivariant reduction of the SO(1,3)
Yang-Mills system on the first two coset spaces yields a mechanical system with
inverted double-well potential and the foliation parameter serving as an
evolution parameter. Its known analytic solutions are periodic or runaway
except for the kink. On the lightcone, only the vacuum solution remains. The
constructed Yang-Mills field strength is singular across the lightcone and of
infinite action due to the noncompact cosets. Its energy-momentum tensor takes
a very simple form, with energy density of opposite signs inside and outside
the lightcone.
