Convection and cracking stability of spheres in general relativity

Abstract

In the present paper we consider convection and cracking instabilities as well as their interplay. We develop a simple criterion to identify equations of state unstable to convection, and explore the influence of buoyancy on cracking (or overturning) for isotropic and anisotropic relativistic spheres. We show that a density profile ρ(r), monotonous, decreasing and concave , i.e. ρ < 0 and ρ < 0, will be stable against convection, if the radial sound velocity monotonically decreases outward. We also studied the cracking instability scenarios and found that isotropic models can be unstable, when the reaction of the pressure gradient is neglected, i.e. δRp = 0; but if it is considered, the instabilities may vanish and this result is valid, for both isotropic and anisotropic matter distributions. * hector@ula.ve †

Anisotropic neutron stars and perfect fluid’s energy conditions

“…(please see Refs. [1][2][3][4][5][6][7][8][9] and the references therein for reviews). The discussions of the relation of the instability of anisotropic stars with perfect fluid energy condition have been reported in Refs.…”

Anisotropic neutron stars by gravitational decoupling

“…which is a linear combination of Eqs. 17, (18) and (19). In this sense, there is no exchange of energy-momentum tensor between the perfect fluid and the anisotropic source and henceforth interaction is purely gravitational.…”

“…(13), (14) and (15), the deformation function f can be found from Eqs. (17), (18) and (19) after choosing suitable conditions on the anisotropic source θ μν . It is worth mentioning that the case we are dealing with demands for an exterior Schwarzschild solution.…”

“…Second, the mimic constrain leads to an simple algebraic equation to solve for the decoupling function f after replacing (27) in (18). In this sense, the only remaining step to construct an anisotropic interior solution following MGD is to choose a suitable perfect fluid as a seed to solve the system (17), (18) and (19) via the mimic constrain to finally obtain the interior solution with local anisotropies described by {ν, λ,ρ,p r ,p ⊥ }.…”

“…However, very few of these solutions can be considered as physically relevant because they violate some of the elementary conditions that a realistic solution has to satisfy (for a list of physical conditions of interior solutions see, for example, [3]). Even more, in the cases where acceptable solutions can be found, the perfect fluid model can not be used to deal with situation where it is assumed local anisotropy of pressure, that seems to be very reasonable for describing the matter distribution under a variety of circumstances [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”