  We study fluid distributions endowed with hyperbolical symmetry, which share
many common features with Lemaitre-Tolman-Bondi (LTB) solutions (e.g. they are
geodesic, shearing, non--conformally flat and the energy density is
inhomogeneous). As such they may be considered as hyperbolically symmetric
versions of LTB, with spherical symmetry replaced by hyperbolical symmetry. We
start by considering pure dust models, and afterwards we extend our analysis to
dissipative models with anisotropic pressure. In the former case the complexity
factor is necessarily non-vanishing, whereas in the latter cases models with
vanishing complexity factor are found. The remarkable fact is that all
solutions satisfying the vanishing complexity condition are necessarily
non-dissipative and satisfy the stiff equation of state.
