I am going to write the perfect fluid gravitational collapse to a particular black hole.
This paper: Article Black hole formation in perfect fluid collapse
might be a good place to start.
For a very good description with references to classical papers (MIsner-Sharp, etc) and numerical solutions, see Sect.8.3 of the book:
Numerical Relativity by T.W. Baumgarte and S. L. Shapiro, Cambridge Univ. Press. 2010.
For dust this was already done in 1933 in a classical paper by Lemaitre (now for some reasons called the Lemaire-Tolman-Bondi model).
Dear Milad,
you will fin about 100 quotation concerning collapsing models at my hp http://members.wavenet.at/arg/PendingPapers/zt.pdf.
Have also a glance on my paper 'Collapsing Schwarzschild interior solution' on researchegate.
Rainer
The collapse condition for non-rotating object is g_00 = 0. The structure of this value is determined by concrete model of collapsing object. The value of g_00 is calculated by means of field equations. The right part of these equations must include energy-momentum tensor describing inner structure of collapsing object. The right part of equations can consist from different energy-momentum tensor if you want take to account electromagnetic field or other effects.
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