Newtonian-like and anti-Newtonian universes

Newtonian-like and anti-Newtonian universes

In an irrotational dust universe, the locally free gravitational field is covariantly described by the gravito-electric and gravito-magnetic tensors Eab and Hab. In Newtonian theory, Hab = 0 and Eab is the tidal tensor. Newtonian-like dust universes in general relativity (i.e. with Hab = 0, often called ‘silent’) have been shown to be inconsistent in general and unlikely to extend beyond the kn...

Anti-Newtonian dynamics

Consider a world in which Newton’s first and second laws hold, but where Newton’s third law takes the form that the forces between any two objects are equal in both magnitude and direction. We will refer to such a world as “antiNewtonian,” although that term has also been used to describe a general relativistic universe with a purely gravitomagnetic field. Violations of Newton’s third law are n...

Post-Newtonian approximation in Maxwell-like form

The equations of the linearized first post-Newtonian approximation to general relativity are often written in ‘‘gravitoelectromagnetic’’ Maxwell-like form, since that facilitates physical intuition. Damour, Soffel, and Xu (DSX) (as a side issue in their complex but elegant papers on relativistic celestial mechanics) have expressed the first post-Newtonian approximation, including all nonlineari...

Incompressible laminar flow - newtonian and non-newtonian fluids

The problems of incompressible flows dominate a large part of the fluid mechanics scene. For this reason, they are given special attention in this book and we devote two chapters to this subject. In the present chapter we deal with various steadystate and transient situations in which the flow is forced by appropriate pressure gradients and boundary forces. In the next chapter we shall consider...

Numerical simulation of Newtonian and non-Newtonian flows in bypass