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Conformally flat spacetimes with an elastic stress energy tensor given by adiagonal trace-free anisotropic pressure tensor are investigated using 1+3formalism. We show how the null tetrad Ricci components are related to thepressure components and energy density. The 1+3 Bianchi and Jacobi identitiesand Einstein field equations are written for this particular case. In generalthe commutators must be considered since they supply potentially newinformation on higher order derivatives of the 1+3 quantities. We solve thesystem for the non rotating case which consist of ODEs of a spatial coordinate.

Studying conformally flat spacetimes with an elastic stress energy tensor using 1+3 formalism