  We study Yang-Baxter deformations of 4D Minkowski spacetime. The Yang-Baxter
sigma model description was originally developed for principal chiral models
based on a modified classical Yang-Baxter equation. It has been extended to
coset curved spaces and models based on the usual classical Yang-Baxter
equation. On the other hand, for flat space, there is the obvious problem that
the standard bilinear form degenerates if we employ the familiar coset
Poincar\'e group/Lorentz group. Instead we consider a slice of AdS$_5$ by
embedding the 4D Poincar\'e group into the 4D conformal group $SO(2,4)$. With
this procedure we obtain metrics and $B$-fields as Yang-Baxter deformations
which correspond to well-known configurations such as T-duals of Melvin
backgrounds, Hashimoto-Sethi and Spradlin-Takayanagi-Volovich backgrounds, the
T-dual of Grant space, pp-waves, and T-duals of dS$_4$ and AdS$_4$. Finally we
consider a deformation with a classical $r$-matrix of Drinfeld-Jimbo type and
explicitly derive the associated metric and $B$-field which we conjecture to
correspond to a new integrable system.
