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We study static solutions of the Tolman--Oppenheimer--Volkoff equations forspherically symmetric objects (stars) living in a space filled with theChaplygin gas. Two cases are considered. In the normal case all solutions(excluding the de Sitter one) realize a three-dimensional spheroidal geometrybecause the radial coordinate achieves a maximal value (the "equator"). Aftercrossing the equator, three scenarios are possible: a closed spheroid having aSchwarzschild-type singularity with infinite blue-shift at the "south pole", aregular spheroid, and a truncated spheroid having a scalar curvaturesingularity at a finite value of the radial coordinate. The second case ariseswhen the modulus of the pressure exceeds the energy density (the phantomChaplygin gas). There is no more equator and all solutions have the geometry ofa truncated spheroid with the same type of singularity. We consider also staticspherically symmetric configurations existing in a universe filled with thephantom Chaplygin gas only. In this case two classes of solutions exist:truncated spheroids and solutions of the wormhole type with a throat. However,the latter are not asymptotically flat and possess curvature singularities atfinite values of the radial coordinate. Thus, they may not be used as models ofobservable compact astrophysical objects.

Tolman-Oppenheimer-Volkoff equations in presence of the Chaplygin gas: stars and wormhole-like solutions