In this paper, we study new exact solutions of Einstein’s field equations
    with the motivation of the relativistic elasticity theory. We construct the
    static conformal elastic solution by applying conformal transformations to the
    Reissner-Nordstr\”{o}m-de Sitter solution. The conformal factors for static
    space-time structure with an elastic matter are obtained. Further, we analyze
    the viability of energy conditions. And also discuss the matching problem with
    the exterior space-time.

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