In this note we wish to complement some recent work in the cosmological literature concerning the Weyl conformal curvature tensor and its parts. In particular, we shall give a clear–cut definition of the Newtonian limits of electric and magnetic parts of the Weyl tensor. We also discuss that only a subset of the relativistic equations is needed to obtain a closed system of equations in the Newt...

The large-scale structure of the Universe is characterized by a web-like structure made of voids, sheets, filaments and knots. The structure of this so-called cosmic web is dictated by the local velocity shear tensor. In particular, the local direction of a filament should be strongly aligned with ê3, the eigenvector associated with the smallest eigenvalue of the tensor. That conjecture is test...

An expression for the divergence of the stress tensor is derived for inhomogeneous suspensions of very long and thin, rigid rods. The stress tensor is expressed in terms of the suspension flow velocity and the probability density function for the position and orientation of a rod. The expression for the stress tensor includes stresses arising from possibly very large spatial gradients in the sh...

Ideal fluid dynamics is studied as a relativistic field theory with particular stress on its hamiltonian structure. The Schwinger condition, whose integrated version yields the stress tensor conservation, is explicitly verified both in equal-time and light-cone coordinate systems. We also consider the hamiltonian formulation of fluids interacting with an external gauge field. The complementary ...

The B (curl) mode of the correlation of galaxy ellipticities (shear) can be used to detect a stochastic gravitational wave background, such as that predicted by inflation. In this paper, we derive the tensor mode contributions to shear from both gravitational lensing and intrinsic alignments, using the gaugeinvariant, full-sky results of Schmidt and Jeong {arXiv:1204.3625 [Phys. Rev. D (to be p...

Experimental results obtained at the Relativistic Heavy Ion Collider (RHIC) have been interpreted in terms of a strongly interacting quark gluon plasma. The strongly interacting plasma is characterized by “perfect fluidity”, i.e. a ratio of shear viscosity to entropy density that saturates a proposed lower bound. In this contribution we explore the possibility that a similar phenomenon takes pl...

We present new analytical self-similar solutions describing a collapse of a massless scalar field in scalar-tensor theories. The solutions exhibit a type of critical behavior. The black hole mass for the near critical evolution is analytically obtained for several scalar-tensor theories and the critical exponent is calculated. Within the framework of the analytical models we consider it is foun...

The condition for the vanishing of the Weyl tensor is integrated in the spherically symmetric case. Then, the resulting expression is used to find new, conformally flat, interior solutions to Einstein equations for locally anisotropic fluids. The slow evolution of these models is contrasted with the evolution of models with similar energy density or radial pressure distribution but non-vanishin...

We derive general covariant expressions for the six independent observable modes of distortion of ideal standard rulers in a perturbed Friedmann-Robertson-Walker spacetime. Our expressions are gauge invariant and valid on the full sky. These six modes are most naturally classified in terms of their rotational properties on the sphere, yielding two scalars, two vector (spin-1), and two tensor (s...

unlike the classical deformation analysis of the earth crust, which derives the planar and vertical strains separately, in this study, we have offered a method for 3-d deformation study based on intrinsic geometry of the manifolds on the topographic surface of the earth. in this way, our method would be based on the 2-d metric tensor of horizontal deformation and 2-d curvature tensor of vertica...