Spherically symmetric perfect fluid in area-radial coordinates
  We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities. 
Hideo Iguchi, Tomohiro Harada, and Filipe C Mena