A new class of spherically symmetric gravitational collapse

We discuss the gravitational collapse of a spherically symmetric perfect fluid distribution of uniformly contracting stars. In a uniformly contracting star, the relative volume element (relative distance in the case of spherical symmetry) between any two neighboring fluid particles is preserved irrespective of the radial coordinate. The physical meaning is that during collapse each small volume element of the fluid distribution preserves its spatial position. This new class of gravitational collapse is analogous to the reverse phenomenon of motion of galaxies during the expansion of the Universe. We discuss the shearing solution of a perfect fluid distribution executing the uniform expansion, which is a scalar and obeys the equation of state $p=p(\rho)$. The field equation is solved in complete generality, such that that the Oppenheimer–Snyder solution with homogeneous density and the Thompson–Whitrow shear-free solution arise as particular cases.