  We present novel neutral and uncharged solutions that describe the cluster of
Einstein in the teleparallel equivalent of general relativity (TEGR). To this
end, we use a tetrad field with non-diagonal spherical symmetry which gives the
vanishing of the off-diagonal components for the gravitational field equations
in the TEGR theory. The clusters are calculated by using an anisotropic
energy-momentum tensor. We solve the field equations of TEGR theory, using two
assumptions: the first one is by using an equation of state that relates
density with tangential pressure while the second postulate is to assume a
specific form of one of the two unknown functions that appear in the
non-diagonal tetrad field. Among many things presented in this study, we
investigate the static stability specification. We also study the
Tolman-Oppenheimer-Volkoff equation of these solutions in addition to the
conditions of energy. The causality constraints with the adiabatic index in
terms of the limit of stability are discussed.
