Related papers: The Inverse Problem for the Euler-Poisson system i…
The effective evolution of an inhomogeneous universe model in Einstein's theory of gravitation may be described in terms of spatially averaged scalar variables. This evolution can be modeled by solutions of a set of Friedmann equations for…
A complete Lagrangian and Hamiltonian description of the theory of self-gravitating light-like matter shells is given in terms of gauge-independent geometric quantities. For this purpose the notion of an extrinsic curvature for a null-like…
We study the evolution of cosmological perturbations, using a hybrid approximation scheme which upgrades the weak-field limit of Einstein's field equations to account for post-Newtonian scalar and vector metric perturbations and for…
Some classical and recent results on the Euler equations governing perfect (incompressible and inviscid) fluid motion are collected and reviewed, with some small novelties scattered throughout. The perspective and emphasis will be given…
The recently introduced relativistic Lagrangian darkon fluid model (EPJ C (2015) 75:9) is generalized to a self-gravitating, irrotational, pressure-less and stress free geodesic fluid, whose energy-momentum tensor is dust-like with…
The Einstein-Vlasov equations govern Einstein spacetimes filled with matter which interacts only via gravitation. The matter, described by a distribution function on phase space, evolves under the collisionless Boltzmann equation,…
Equations of non-geodesic and non-geodesic deviations for different particles are obtained, using a specific type of classes of the Bazanski Lagrangian. Such type of paths has been found to describe the problem of variable mass in the…
This paper presents a study of the isosceles problem resulting by a perturbation of Euler's collinear solution under Newtonian gravitational attraction of three bodies in space. After the Hamiltonian was obtained, a circumference of…
Owing to the renewed interest in dark matter after the upgrade of the large hadron collider and its dedication to dark matter research it is timely to reassess the whole problem. Considering dark matter is one way to reconcile the…
A new theory for determining the mass function of cosmic structures is presented. It relies on a realistic treatment of collapse dynamics. Gravitational collapse is analyzed in the Lagrangian perturbative framework. Lagrangian perturbations…
This paper has been withdrawn by the author after further work showed the proposed theoretical approach cannot fit planetary perihelion precession data. As presented, the theory doesn't fit gravitational light deflection by the sun either,…
The Einstein initial-value equations in the extrinsic curvature (Hamiltonian) representation and conformal thin sandwich (Lagrangian) representation are brought into complete conformity by the use of a decomposition of symmetric tensors…
We study the relativistic Euler equations on the Minkowski spacetime background. We make assumptions on the equation of state and the initial data that are relativistic analogs of the well-known physical vacuum boundary condition, which has…
This paper concerns the classical dynamics of three coupled rotors: equal masses moving on a circle subject to attractive cosine inter-particle potentials. It is a simpler variant of the gravitational three-body problem and also arises as…
We deal with a dynamical mechanism in which a large cosmological constant, as suggested by inflationary scenarios, decays due to expansion of the universe. This mechanism has its origin in the gravitational coupling of the vacuum density.…
We derive the geodesic equation of motion in the presence of weak gravitational fields produced by relativistic sources such as cosmic strings, decomposed into scalar, vector and tensor parts. We find that the vector (gravito-magnetic)…
We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive…
Dark matter, a conjectured substance not directly observable but which has tremendous mass, was proposed to explain why galaxies hold together and rotate faster at their edges than predicted by Newton's Inverse Square (1/r2) Law of Gravity.…
The Standard Model of particle physics is a $SU(3)_c\times SU(2)_L\times U(1)_Y$ gauge theory that can explain the strong, weak, and electromagnetic interactions between the particles. The gravitational interaction is described by…
The low-lying eigenstates of a one-dimensional (1D) system of many impenetrable point bosons and one moving impurity particle with repulsive zero-range impurity-boson interaction are found for all values of the impurity-boson mass ratio and…