A charged perfect fluid model with high compactness

Abstract

A relativistic, static and spherically symmetrical stellar model is presented, constituted by a perfect charged fluid. This represents a generalization to the case of a perfect neutral fluid, whose construction is made through the solution to the Einstein-Maxwell equations proposing a form of gravitational potential $g_{tt}$ and the electric field. The choice of electric field implies that this model supports values of compactness$u=GM/c^2R\leq 0.5337972212$, values higher than the case without electric charge ($u\leq 0.3581350065$), being this feature of relevance to get to represent compact stars. In addition, density and pressure are positive functions, bounded and decreasing monotones, the electric field is a monotonously increasing function as well as satisfying the condition of causality so the model is physically acceptable. In a complementary way, the internal behavior of the hydrostatic functions and their values are obtained taking as a data the corresponding to a star of $1 M_\odot$,for different values of the charge parameter, obtaining an interval for the central density $\rho_c\approx (7.9545,2.7279) 10^{19}$ $ Kg/m^3$ characteristic of compact stars.

Generating solutions for charged stellar models in general relativity

“…Solutions with given Δ, a 1 and l are discussed [41][42][43], where the mass is used instead of y, [44][45][46][47][48][49][50]. There are also solutions with Δ = 0 [51,52].…”

“…Together, Eqs. (51,52) give another linear equation for y which depends only on a 1 and Δ. Solving it, we find y and then l 2 from any of Eqs.…”

On quintessence star model and strange star

“…Since σ = k R 2 B g > 0 this relation determines the values of the MIT Bag constant given ν. Replacing (31) in Eq. 30we arrive at the finding that the rate of compactness u for this model matches the one obtained for the case of a perfect fluid with (y, B), given by (22) and 21…”

“…We know that its mass is M = 0.87M and its radius R = 7.866km, replacing this in (32) we obtain (ν = 0.51192), and replacing this value in Eq. (31) and since σ = k R 2 B g we determine the value of B g to be B g = 97.00476509 Mev fm 3 . The value that we obtained differs a little from the one obtained previously for the same star, considering a model without quintessence, which was B g = 99.7207866 Mev/fm 3 [66] .…”

“…On the other hand there have been some approaches at a stellar level to describe compact objects [20][21][22][23], considering that the interior of the stars is formed by ordinary neutral matter [24][25][26][27][28][29][30], ordinary charged matter [31][32][33][34][35][36][37], and also by sources which are a combination of ordinary matter and quintessence dark energy, consistent with neutron stars [38]. Neutron or quark stars are not exclusively composed of neutrons or quarks, respectively, but rather these stars are formed predominantly by one of those particles.…”