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

### 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.Comment: 12 pages, 8 figure

Topics: General Relativity and Quantum Cosmology
Publisher: 'Springer Science and Business Media LLC'
Year: 2020
DOI identifier: 10.1140/epjc/s10052-021-08894-3
OAI identifier: oai:arXiv.org:2006.10561

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