Standard notation and terminology of differential geometry and general relativity are used in this article. All considerations are local so that the four-dimensional space-time M is assumed to be a smooth manifold diffeomorphic to R4. It is endowed with a metric tensor g of signature (1, 3) and a linear connection defining the covariant differentiation of tensor fields. Greek indices range from...

The asymptotic behaviour of the components of the Weyl tensor and of the energy-momentum tensor in the Penrose limit is determined. In both cases a peeling-off property is found. Examples of different types of matter are provided. The expansion and shear of the congruence of null geodesics along which the Penrose limit is taken are determined. Finally, the approach to the singularity in the Pen...

astrophysics is becoming now an integral part of general physics. considering the black hole theory ,which is a new and exciting branch of relativistic astrophysics, we see many connections between elementary particle physics and astrophysics. in this article we attempt to explain the development of star physics ,in an easy ,understandable manner. previous knowledge of relativistic theory or cl...

The post-Newtonian hydrodynamic equations for a non-perfect fluid are developed within the framework of Boltzmann equation. components energy–momentum tensor determined by considering relativistic Eckart decomposition viscous and heat conducting fluid. From Grad distribution function its expression is derived. mass density, mass-energy density momentum from transfer equation Grad’s function. In...

In generalizing the special-relativistic one-component version of Eckart’s continuum thermodynamics to general-relativistic space-times with Riemannian or post-Riemannian geometry as presented by Schouten (Schouten, J.A. Ricci-Calculus, 1954) and Blagojevic (Blagojevic, M. Gauge Theories of Gravitation, 2013) we consider the entropy production and other thermodynamical quantities, such as the e...

In this paper and its companion [2], the authors introduce a causal hyperbolic modification of the Eckart-Landau-Weinberg dissipation tensor, for the dynamics of collision-dominated radiation. The resulting system of partial differential equations for relativistic fluid dynamics is shown to exclusively admit subluminal, decaying modes for any finite wavelength. This validates the new relativist...

in which the WA are the components of the unit time-like velocity vector and the quantities hAB are the components of the metric tensor of the space. The scalar p in these equations is the material density and is assumed to satisfy a conservation law; finally, the quantity p is a scalar which is commonly called the pressure although it is not to be confused with a hydrodynamical pressure. A str...

The apparent shear viscosity, in the non-Browman Ilmit, for a homogeneous suspension of monodispersed hard spheres in systems ranging from dilute to concentrated was previously established. From an estimation of the viscous dissipation. We use the inter-particle distance dependence of the shear viscosity for determining the components of a local stress tensor associated with the transient netwo...

In all media in which the elastic stiffness tensor and density vary in space, an implicit, frequency-dependent anisotropy is present, even if the medium is locally isotropic. This predicts a non-linear, frequency-dependent polarization of body waves, and explains shear-wave splitting in heterogeneous media. Examples are presented for compressional and shear waves in a medium in which the elasti...

Few recent generations of cosmologists have solved non-local newtonian equations of the gravitational instability in an expanding universe. In this approach pancaking is the predominant form of first collapsing objects. Relativistic counterparts of these equations contain the electric and magnetic parts of the Weyl tensor. In the linear theory the magnetic part is associated with gravitational ...