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.

arXiv comment12 pages, 8 figures

References in corpus (18)

• Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations
• Static charged perfect fluid spheres in general relativity
• A class of relativistic stars with a linear equation of state
• Electric fields at the quark surface of strange stars in the color-flavor locked phase
• Sharp bounds on the critical stability radius for relativistic charged spheres
• Sharp bounds on $2m/r$ of general spherically symmetric static objects
• Minimum mass-radius ratio for charged gravitational objects
• The role of pressure anisotropy on the maximum mass of cold compact stars
• Maximum Mass-Radius Ratios for Charged Compact General Relativistic Objects
• Tikekar superdense stars in electric fields
• Space-time inhomogeneity, anisotropy and gravitational collapse
• On the gravitational field of a sphere of incompressible fluid according to Einstein's theory
• Sharp bounds on 2m/r for static spherical objects
• Absolute Stability Limit for Relativistic Charged Spheres
• Charged Vaidya-Tikekar model for super compact star
• Relativistic Solution for a Class of Static Compact Charged Star in Pseudo Spheroidal Space-Time
• Non-adiabatic radiative collapse of a relativistic star under different initial conditions
• Higher dimensional generalization of Buchdahl-Vaidya-Tikekar model for super compact star

Cited by in corpus (5)

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• Horndeski fermion-boson stars
• Compact stars in the Einstein dark energy model