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The gravitational collapse of a star is a warmly discussed but still puzzling problem, which not only involves the dynamics of the gases, but also the subtle coordinate transformation. In this letter, we give some more detailed investigation on this problem, and reach the results: (I). The comoving coordinate system for the stellar system is only compatible with the zero-pressure free falling particles. (II). For the free falling dust, there are three kind of solutions respectively corresponding to the oscillating, the critical and the open trajectories. The solution of Oppenheimer and Snyder is the critical case. (III). All solutions are exactly derived. There is a new kind singularity in the solution, but its origin is unclear.
Spherically gravitational collapse towards a black hole with non-zero tangential pressure is studied. Exact solutions corresponding to different equations of state are given. We find that when taking the tangential pressure into account, the exact so
This paper presents a general averaging procedure for a set of observers which are tilted with respect to the cosmological matter fluid. After giving the full set of equations describing the local dynamics, we define the averaging procedure and apply
The isothermal Tolman condition and the constancy of the Klein potentials originally expressed for the sole gravitational interaction in a single fluid are here generalized to the case of a three quantum fermion fluid duly taking into account the str
Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens object [Phys.
Obtaining exact solutions of the spherically symmetric general relativistic gravitational field equations describing the interior structure of an isotropic fluid sphere is a long standing problem in theoretical and mathematical physics. The usual app