We investigate spherically symmetric gravitational collapse of thick matter
shell without radiation in the Einstein gravity with cosmological constant. The
orbit of the infalling thick matter is determined by imposing an equation of
state for the matter near interface, where pressure constituted of the
transverse component and the longitudinal one is proportional to energy
density. We present analytic solutions for the equation of state and discuss
parameter region to satisfy physical conditions such as the absence of the
shell crossing singularity, the monotonic increase of the emergent infinite
redshift surface and energy conditions. We finally show that adopting the
definition presented in arXiv:2005.13233 the total energy in this
time-dependent system is invariant under the given time evolution.
