  This paper analyzes the supersymmetric solutions to five and six-dimensional
minimal (un)gauged supergravities for which the bilinear Killing vector
constructed from the Killing spinor is null. We focus on the spacetimes which
admit an additional ${\rm SO}(1,1)$ boost symmetry. Upon the toroidal
dimensional reduction along the Killing vector corresponding to the boost, we
show that the solution in the ungauged case describes a charged, nonextremal
black hole in a Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe with an
expansion driven by a massless scalar field. For the gauged case, the solution
corresponds to a charged, nonextremal black hole embedded conformally into a
Kantowski-Sachs universe. It turns out that these dimensional reductions break
supersymmetry since the bilinear Killing vector and the Killing vector
corresponding to the boost fail to commute. This represents a new mechanism of
supersymmetry breaking that has not been considered in the literature before.
