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In this work, we use the distribution formalism to derive the full set ofjunction conditions for general Local Rotational Symmetric (LRS) spacetimes inthe $1+1+2$ covariant formalism. We start by developing a framework on which asingle parameter controls the type of hypersurface separating the twospacetimes to be matched, i.e., timelike, spacelike, or null hypersurfaces, andobtain the extrinsic curvature of such a surface as a function of thisparameter. We then introduce the distribution formalism in the $1+1+2$equations and obtain the necessary conditions to preserve the regularity ofthese equations at the separation hypersurface, which are equivalent to thejunction conditions in General Relativity. As examples of applications, we usethis formalism to perform the matching for the Martinez thin-shell, theSchwarzschild constant-density fluid star, and the Oppenheimer-Snyder collapse.

Junction conditions for general LRS spacetimes in the $1+1+2$ covariant formalism