  In Einstein theory of gravity the initial configuration of metric field and
its time derivative are related to matter configuration by four equations
called constraints. We use the method of conformal metrics (York Method) to
solve constraints and find an analytic set of consistent initial data for
linearized Einstein field equations in a perturbed constant curvature
space-time. They are explicitly covariant and more compact than decomposition
of quantities to scalar, vector and tensor. This method is independent of type
and physics of matter fields and is extendable to higher-order perturbative
calculations. As an application example, we apply this method to two commonly
used matching conditions during a phase transition and compare and interpret
the results.
