Neutral physical compact spherically symmetric stars with non-exotic matters in Einstein’s cluster model using Weitzenböck geometry

Abstract

Abstract 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 $$ however \, \,in\, \,this\, \,study\, \,we\, \,constrain\,\, the\,\, constants \, \,of\, \, integration\, \, from\, \, \,the\, \, matching\,\, of\, \,boundary $$ h o w e v e r i n t h i s s t u d y w e c o n s t r a i n t h e c o n s t a n t s o f i n t e g r a t i o n f r o m t h e m a t c h i n g o f b o u n d a r y $$ condition\, \, in a\,\, way \,\,different\,\, from\,\, that\,\, presented \,\,in \,\,the\,\, literature. $$ c o n d i t i o n i n a w a y d i f f e r e n t f r o m t h a t p r e s e n t e d i n t h e l i t e r a t u r e . 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.