An electromagnetic extension of the Schwarzschild interior solution and the corresponding Buchdahl limit

We wish to construct a model for charged star as a generalization of the uniform density Schwarzschild interior solution. We employ the Vaidya and Tikekar ansatz (Astrophys Astron 3:325, 1982) for one of the metric potentials and electric field is chosen in such a way that when it is switched off the metric reduces to the Schwarzschild. This relates charge distribution to the Vaidya–Tikekar parameter, k, indicating deviation from sphericity of three dimensional space when embedded into four dimensional Euclidean space. The model is examined against all the physical conditions required for a relativistic charged fluid sphere as an interior to a charged star. We also obtain and discuss charged analogue of the Buchdahl compactness bound.

RELATIVISTIC SOLUTION FOR A CLASS OF STATIC COMPACT CHARGED STAR IN PSEUDO-SPHEROIDAL SPACETIME

Considering Vaidya–Tikekar metric, we obtain a class of solutions of the Einstein–Maxwell equations for a charged static fluid sphere. The physical 3-space (t = const. ) here is described by pseudo-spheroidal geometry. The relativistic solution for the theory is used to obtain models for charged compact objects; thereafter, a qualitative analysis of the physical aspects of compact objects are studied. The dependence of some of the properties of a superdense star on the parameters of the three geometry is explored. We note that the spheroidicity parameter a plays an important role for determining the properties of a compact object. A nonlinear equation of state (EOS) is required to describe a charged compact object with pseudo-spheroidal geometry, which we have shown for known masses of compact objects. We also note that the size of a static compact charged star is more than that of a static compact star without charge.