On spherically symmetric shear-free perfect fluid configurations (neutral and charged). I

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Abstract
A class of solutions describing a wide variety of nonstatic, spherically symmetric, charged, shear-free perfect fluid configurations is derived. It is presented in the form of Jacobian elliptic functions characterized by seven free parameters: five constants and two arbitrary functions of time. This class of solutions is the most general charged version of the class derived by Kustaanheimo and Qvist [Comment. Phys. Math. Helsingf. 13, 12 (1948); Exact Solutions of Einstein’s Field Equations (Cambridge U. P., Cambridge, 1980), Chap. 12, Sec. 2]. It is found that many of the charged particular solutions expressible by elementary functions are new. Particular solutions, including neutral and uniform density solutions, are classified in detail. The physical interpretation of these solutions, including the study of their singularity structure, will be presented in a subsequent paper (Part II).