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;

We argue that combined observations of galaxy rotation curves and gravitational lensing not only allow the deduction of the mass profile of a galaxy, but also yield information about the pressure in the galactic fluid. We quantify this statement by enhancing the standard formalism for rotation curve and lensing measurements to a first post‐Newtonian approximation. This enhanced formalism is compatible with currently employed and established data analysis techniques, and can in principle be used to reinterpret existing data in a more general context. The resulting density and pressure profiles from this new approach can be used to constrain the equation of state of the galactic fluid, and therefore might shed new light on the persistent question of the nature of dark matter.

The pair separation model of Goto and Vassilicos ͓New J. Phys. 6, 65 ͑2004͔͒ is revisited and placed on a sound mathematical foundation. A direct numerical simulation of two-dimensional homogeneous isotropic turbulence with an inverse energy cascade and a k −5/3 power law is used to investigate properties of pair separation in two-dimensional turbulence. A special focus lies on the time asymmetry observed between forward and backward separations. Application of the present model to these data suffers from finite inertial range effects and thus, conditional averaging on scales rather than on time has been employed to obtain values for the Richardson constants and their ratio. The Richardson constants for the forward and backward case are found to be ͑1.066Ϯ 0.020͒ and ͑0.999Ϯ 0.007͒, respectively. The ratio of Richardson constants for the backward and forward cases is therefore g b / g f = ͑0.92Ϯ 0.03͒, and hence exhibits a qualitatively different behavior from pair separation in three-dimensional turbulence, where g b Ͼ g f ͓J. Berg et al., Phys. Rev. E 74, 016304 ͑2006͔͒. This indicates that previously proposed explanations for this time asymmetry based on the strain tensor eigenvalues are not sufficient to describe this phenomenon in two-dimensional turbulence. We suggest an alternative qualitative explanation based on the time asymmetry related to the inverse versus forward energy cascade. In two-dimensional turbulence, this asymmetry manifests itself in merging eddies due to the inverse cascade, leading to the observed ratio of Richardson constants.

Gravitational lensing in a weak but otherwise arbitrary gravitational field can be described in terms of a 3 × 3 tensor, the "effective refractive index". If the sources generating the gravitational field all have small internal fluxes, stresses, and pressures, then this tensor is automatically isotropic and the "effective refractive index" is simply a scalar that can be determined in terms of a classic result involving the Newtonian gravitational potential. In contrast if anisotropic stresses are ever important then the gravitational field acts similarly to an anisotropic crystal. We derive simple formulae for the refractive index tensor, and indicate some situations in which this will be important.