Gravastars must have anisotropic pressures

Abstract

One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the "gravastar" model developed by Mazur and Mottola; and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure -without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluidsanisotropic pressures in the "crust" of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl-Bondi bound for perfect fluid stars. Finally we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation. gr-qc/0505137;

Slowly rotating supercompact Schwarzschild stars

“…which indicates an anisotropy in pressure at the singular surface r = R 0 (see also [16]). It is this δ-function integrable through the Komar formula, together with the relaxation of the isotropic perfect fluid condition at r = R 0 that provide a physical interpretation of the Schwarzschild star in the regime R ≤ (9/8)R S .…”

“…By contraction of the Ricci tensor, we obtain the Ricci scalar or curvature scalar 16) which corresponds to the trace of the Ricci tensor. From its symmetries, the Riemann tensor has 1 12 n 2 (n 2 − 1) algebraically independent components, where n is the dimension of the space.…”

“…From the TOV equation (2.5), it can be shown that these discontinuities can be avoided if there is an infinitesimal thin-shell with anisotropic pressures p ⊥ = p [16]. One of the advantages of these anisotropic pressures, is their continuity, although we still need to specify an EOS.…”

Anisotropic extension of Finch and Skea stellar model

“…Scalar field 'boson stars' are naturally anisotropic (Schunch (2003)). Wormholes (Morris and Thorne (1988)) and gravastars (Cattoen et al (2005); DeBenedictis et al (2006)) have also anisotropic characteristics. Ivanov (2010) has pointed out that incorporation of the electromagnetic field into a relativistic stellar object has an anisotropic interpretation.…”

Physics of Accretion Flows around Compact Objects

“…Since this surface is at Rg * = RS(1 + ǫ) gravastar sizes are not restricted by the Buchdahl-Bondi [47] [48] bound 2 (R * > 9/8RS, or the redshift z > 0.33 -for comparison the maximum redshift of a neutron star is 0.851 [78]) their ridiculously large redshifts make them apparently indistinguishable from black holes, hence their potential astrophysical interest [2]. Such compactness is achieved at a price: to avoid the presence of naked singularities gravastars must have anisotropic pressures and a very peculiar equation of state [50]. Of course if one accepts negative central pressures and violation of the dominant energy condition (which requires ρ ≥ 0; |p| ≤ ρ) this cannot be the reason to dismiss dark energy stars (incidentally, but not accidentally, "normal" boson stars are subject to anisotropic stress and cannot be described by an equation of state [38]).…”