Related papers: Double layer in quadratic gravity and least action…
Starting from the original Einstein action, sometimes called the Gamma squared action, we propose a new setup to formulate modified theories of gravity. This can yield a theory with second order field equations similar to those found in…
We present the most general actions of a single scalar field and two scalar fields coupled to gravity, consistent with second order field equations in four dimensions, possessing local scale invariance. We apply two different methods to…
A classical and a relativistic law of motion for an advancing shell are deduced applying the thin layer approximation. A new parameter connected with the quantity of absorbed matter in the expansion is introduced; this allows of matching…
We present, for the first time, an action principle that gives the equations of motion of an extended body possessing multipole moments in an external gravitational field, in the weak field limit. From the action, the experimentally…
A nonlinear sea-ice problem is considered in a least-squares finite element setting. The corresponding variational formulation approximating simultaneously the stress tensor and the velocity is analysed. In particular, the least-squares…
It is shown that for a relativistic particle moving in an electromagnetic field its equations of motion written in a form of the second law of Newton can be reduced with the help of elementary operations to the Hamilton-Jacobi equation. The…
Generalized differential forms are employed to construct generalized connections. Lorentzian four-metrics determined by certain of these connections satisfy Einstein's vacuum field equations when the connections are flat. Generalized…
The problem of the description of two interacting particles is considered. It is shown that it can be reduced to the description of one particle in an external static potential even in a relativistic case. The method is based on the…
As a supersymmetric extension of the Randall-Sundrum model, we consider a 5-dimensional Horava-Witten type theory, and derive its low energy effective action. The model we consider is a two-brane system with a bulk scalar field satisfying…
The interactions inside the (bisemi)particles are envisaged from two points of view: The first approach, based on the reducible representations of algebraic bilinear semigroups, allows to describe explicitly the interactions between…
By a spherical gravitating condenser we mean two concentric charged shells made of perfect fluids restricted by the condition that the electric field is nonvanishing only between the shells. Flat space is assumed inside the inner shell. By…
This comment contains a suggestion for a slight modification of Israel's covariant formulation of junction conditions between two spacetimes, placing both sides on equal footing with normals having uniquely defined orientations. The signs…
The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in ${{e^{-\Phi}}\over {g_4^2}}$ by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the…
As in the case of Einstein or Lovelock gravity, the action of quartic quasitopological gravity has not a well-defined variational principle. In this paper, we first introduce a surface term that makes the variation of quartic…
We perform an analysis where Einstein's field equation is derived by means of very simple thermodynamical arguments. Our derivation is based on a consideration of the properties of a very small, spacelike two-plane in a uniformly…
We discuss Israel layers collapsing inward from rest at infinity along Schwarzschild-Lemaitre geodesics. The dynamics of the collapsing layer and its equation of state are developed. There is a general equation of state which is…
A scheme is developed which enables one to trace backwards in time the cosmic density and velocity fields, and to determine accurately the current-epoch velocity field from the current-epoch density field, or vice versa. The scheme…
As is well known, in order for the Einstein--Hilbert action to have a well defined variation, and therefore to be used for deriving field equation through the stationary action principle, it has to be amended by the addition of a suitable…
The spherically symmetric thin shells are the nearest generalizations of the point-like particles. Moreover, they serve as the simple sources of the gravitational fields both in General Relativity and much more complex quadratic gravity…
The microscopic theories of quantum gravity related to integrable lattice models can be constructed as special deformations of pure gravity. Each such deformation is defined by a second order differential operator acting on the coupling…