https://doi.org/10.1140/epjc/s10052-020-08671-8
Regular Article – Theoretical Physics
Neutral physical compact spherically symmetric stars with non-exotic matters in Einstein’s cluster model using Weitzenböck geometry
1
Centre for Theoretical Physics, The British University in Egypt, P.O. Box 43, 11837, El Sherouk City, Cairo, Egypt
2
Egyptian Relativity Group (ERG), Cairo University, 12613, Giza, Egypt
3
Center for Space Research, North-West University, 2745, Mahikeng, South Africa
4
Division of Human Support System, Faculty of Symbiotic Systems Science, Fukushima University, 960-1296, Fukushima, Japan
Received:
16
September
2020
Accepted:
13
November
2020
Published online:
3
December
2020
We revisit the neutral (uncharged) solutions that describe Einstein’s clusters with matters in the frame of Weitzenböck geometry. To this end, we use a tetrad field with non-diagonal spherical symmetry which gives vanishing of the off-diagonal components of the gravitational field equations. The cluster solutions are calculated by using an anisotropic energy–momentum tensor. We solve the field equations using two novel assumptions. First, we use an equation of state that relates density with tangential pressure, and then we assume a specific form of one of the metric potentials in addition to the assumption of the vanishing of radial pressure to make the system of differential equations in a closed-form. The resulting solutions are coincide with the literature 
Among many things presented in this study, we investigate the static stability specification and show that our model is consistent with a real compact start except that the tangential pressure has a vanishing value at the center of the star which is not accepted from the physical viewpoint of a real compact star. We conclude that the model that has vanishing radial pressure in the frame of Einstein’s theory is not a physical model. Therefore, we extend this study and derive a new compact star without assuming the vanishing of the redial pressure but instead we assume new form of the metric potentials. We repeat our procedure done in the case of vanishing radial pressure and show in details that the new compact star is more realistic from different physical viewpoints of real compact stellar.
© The Author(s) 2020
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3
