| Abstract: | An in-depth study of various methods, and their correlations, of obtaining exact solutions of Einstein-Maxwell field equations representing shear free motion of spherically symmetric charged perfect fluid distributions has been made. It is shown that one can employ isotropic coordinate systems without any loss of generality. However the investigations have been carried out in an arbitrary coordinate system. The exact solutions relating to simple situations viz. (i) homogeneous density distribution, ϱ=ϱ(t), (ii) conformally flat solutions and (iii) distributions obeying an equation of state, p=p(ϱ) are briefly discussed. The methods due to MCVITTIE (1967), introduced initially for neutral fluids, and MASHHON and PARTOVI (1979) where one assumes the metric in a convenient form form one group and the methods due to SHAH and VAIDYA (1968), CHAKRAVARTY and CHATTERJEE (1978), CHATTERJEE (1984) and SUSSMAN (1987) where one chooses suitably two arbitrary functions of integration form the other group. This splitting of various methods into two is based on the earlier analogous work for the neutral fluids due to SRIVASTAVA (1987). Using McVittie's procedure we obtain a solution which in its uncharged limit reduces to Friedmann-Robertson-Walker solution whereas for non-vanishing charge is equivalent to the solution due to SHAH and VAIDYA (1967). This solution is termed as generalised Shah-Vaidya solution or charged Friedmann-Robertson-Walker solution. A suitable generalisation of Mashhoon and Partovi's procedure has been found to contain MASHHOON-PARTOVI solution (1979) and SHAH-VAIDYA solution (1967) as members of a class. The method employed by CHATTERJEE (1978), which does not yield the general solution of the problem, has been shown to lead to the procedure adopted by SUSSMAN (1987) after it is generalised suitably. The McVittie type and Wyman type solutions introduced by Sussman has been found to be contained in McV class of metries discussed here. It is also found that solutions obtained by CHAKRAVARTY and CHATTERJEE (1978) represent a class of charged Kustaanheimo-Qvist solution which are expressible as elementary functions. Finally, all known solutions have been derived introducing an adhoc assumption in the form of a mathematical relation and searching for the solutions free from movable critical points. |
