where τ τ 0 ( R ) emerges as another arbitrary function. However, we know that centrally symmetric matter distribution can be described by at most two functions, namely their density distribution and the radial velocity of the matter. This means that of the three functions f , F , τ τ 0 , only two are independent. In fact, since no particular selection has been made for the Lagrangian coordinate R yet that can be subjected to arbitrary transformation, we can see that only two functions are arbitrary. For the dust-like medium, there exists another solution where r = r ( τ τ ) and independent of R , although such solution does not correspond to collapse of a finite body of matter.