  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 $\omega$.
