Acceptability conditions and relativistic anisotropic generalized polytropes

Abstract

This paper explored the physical acceptability conditions for anisotropic matter configurations in General Relativity. The study considered a generalized polytropic equation of state $$P=\kappa {\rho }^{\gamma }+\alpha \rho -\beta $$ P = κ ρ γ + α ρ - β for a heuristic anisotropy. We integrated the corresponding Lane–Emden equation for several hundred models and found the parameter-space portion ensuring the physical acceptability of the configurations. Polytropes based on the total energy density are more viable than those with baryonic density, and small positive local anisotropies produce acceptable models. We also found that polytropic configurations where tangential pressures are greater than radial ones are also more acceptable. Finally, convective disturbances do not generate cracking instabilities. Several models emerging from our simulations could represent candidates of astrophysical compact objects.

Uncharged and charged anisotropic like-Durgapal stellar models with vanishing complexity

“…Moreover, at the centre, they satisfy e −λ(0) = 1 and e ν(0) = const. From this we can observe a monotonously increasing correct behavior for the mass function, this is consistent with the adequate behavior of the metric function λ [72][73][74]. Now, in figures 3, 4 and 5 we show the behavior of the matter sector (thermodynamic variables) plotted as a function of the radial coordinate r using R = 1.…”

Acceptability Conditions and Relativistic Barotropic Equations of State

“…Notice that the standard 2m/r < 1 condition is different from the stronger (m/r) > 0, as required by B.V. Ivanov in [35]. Clearly, if (m/r) > 0 we obtain well behaved metric functions but, there are cases with (m/r) < 0 having physically reasonable metric coefficients [52]. Thus, (m/r) > 0 should be considered as a sufficient but not a necessary condition to obtain "well behaved" metric potentials.…”

Integration of the Lane–Emden equation for relativistic anisotropic polytropes through gravitational decoupling: a novel approach

“…This is so, given that the g tt metric component is known since it corresponds to the metric function of the seed solution. Thus, replacing (18) in (57) and using (30), we arrive at…”

“…In the general relativistic regime, polytropes also have been extensively studied (see, for example, [8][9][10][11][12][13][14][15] and the references therein. For more recent works see [16][17][18], for example). a e-mail: ernesto.fuenmayor@ciens.ucv.ve b e-mail: econtreras@usfq.edu.ec (corresponding author)…”