Gorenstein projective modules and recollements over triangular matrix rings

Let $T=left( begin{array}{cc} R & M 0 & S end{array} right) $ be a triangular matrix ring with $R$ and $S$ rings and $_RM_S$ an $R$-$S$-bimodule. We describe Gorenstein projective modules over $T$. In particular, we refine a result of Enochs, Cort{e}s-Izurdiaga and Torrecillas [Gorenstein conditions over triangular matrix rings, J. Pure Appl. Algebra 218 (2014), no. 8, 1544-1554]. Also, we consider when the recollement of $mathbb{D}^b(T{text-} Mod)$ restricts to a recollement of its subcategory $mathbb{D}^b(T{text-} Mod)_{fgp}$ consisting of complexes with finite Gorenstein projective dimension. As applications, we obtain recollements of the stable category $underline{T{text-} GProj}$ and recollements of the Gorenstein defect category $mathbb{D}_{def}(T{text-} Mod)$.