We study singularity categories through Gorenstein objects in triangulated categories and silting theory. Let ${ \omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\mathcal{ T}$. We introduce the notion of $\omega$-Gorenstein objects, which is far extended version of Gorenstein projective modules and Gorenstein injective modules in triangulated categories. We prove that the stable category $\underline{ \mathcal{ G}_{ \omega}}$, where $\mathcal{ G}_{ \omega}$ is the subcategory of all ${ \omega}$-Gorenstein objects, is a triangulated category and it is, under some conditions, triangle equivalent to the relative singularity category of $\mathcal{ T}$ with respect to $\omega$.
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