Conformal geodesics in spherically symmetric vacuum spacetimes with cosmological constant

An analysis of conformal geodesics in the Schwarzschild-de Sitter and Schwarzschild-anti-de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that the congruence of conformal geodesics arising from this data cover the whole maximal extension of canonical conformal representations of the spacetimes without forming caustic points. For the Schwarzschild-de Sitter family, the resulting congruence can be used to obtain global conformal Gaussian systems of coordinates of the conformal representation. In the case of the Schwarzschild-anti-de Sitter family, the natural parameter of the curves only covers a restricted time span so that these global conformal Gaussian systems do not exist.