Authors: Petarpa Boonserm, Napasorn Jongjittanon and Tritos Ngampitipan
Abstract: A perfect fluid sphere is one of the established assumptions to reduce the complexity of the Einstein field equation so that an exact solution can possibly be obtained. However, a perfect fluid sphere is not realistic because most stars in the universe are composed of charges. From the perspective of spacetime geometry, the presence of charge makes fluid pressure anisotropic. The condition for charged fluid sphere, in terms of an ordinary differential equation, is different from a perfect fluid sphere. From the perspective of matter, the central equation is the Tolman-Oppenheimer-Volkov (TOV) equation. The presence of charge modifies the TOV equation. In this paper, we de velop new generating theorems, both in the view of the spacetime geometry and in the view of matter. For spacetime geometry, we develop two new theorems using the corresponding ordinary differential equation and apply them to the Reissner- Nordstrom metric. For matter, we develop two new theorems using the corresponding modified TOV equation. Moreover, the effect of charge on fluid density, in case of constant pressure, is also investigated. The results show that the fluid density decreases as the charge density increases, to keep the pressure constant.
Keywords: anisotropy; charged fluid sphere; Einstein- Maxwell field equation; modified TOV equation; solution generating theorem