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

TL;DR

This paper develops a charged star model extending the Schwarzschild interior solution by incorporating electromagnetic fields, analyzing its physical viability, and deriving a charged version of the Buchdahl limit for compactness.

Contribution

It introduces a novel charged star model based on the Vaidya-Tikekar ansatz and derives a new Buchdahl limit considering electric charge effects.

Findings

Model satisfies physical conditions for charged fluid spheres.

Derived a charged Buchdahl compactness bound.

Relates charge distribution to space deviation parameter.

Abstract

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 [{\it Astrophys. Astron.} {\bf 3} (1982) 325] 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 form 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.