Gorenstein projective modules and recollements over triangular matrix rings

Let $T=\left( \begin{array}{cc} R & M 0 & S \end{array} \right) $beatriangularmatrixringwith$R$and$S$ringsand$_RM_S$an$R$-$S$-bimodule\mathrm{.}WedescribeGorensteinprojectivemodulesover$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 $\underset{‾}{T\text{-}GProj}$ and recollements of the Gorenstein defect category ${\mathbb{D}}_{def}(T\text{-}Mod)$.