Related papers: The rocket problem in general relativity
The standard energy conditions of classical general relativity are applied to FLRW cosmologies containing sudden future singularities. Here we show, in a model independent way, that although such cosmologies can satisfy the null, weak and…
The minimum-fuel low-thrust transfer between circular orbits is formulated using the Edelbaum's averaged dynamics with the addition of the nodal precession due to the first zonal term. The extremal analysis shows that an optimal transfer is…
Gravitational repulsion is an inherent aspect of the Schwarzschild solution of the Einstein-Hilbert field equations of general relativity. We show that this circumstance means that it is possible to gravitationally accelerate particles to…
This exploration of solutions for the orbits of Local Group galaxies under the cosmological initial condition of growing peculiar velocities and fitted to measured distances, redshifts, and proper motions reveals a considerable variety of…
The late-time cosmic acceleration may be due to infra-red modifications of General Relativity. In particular, we consider a maximal extension of the Hilbert-Einstein action and analyze several interesting features of the theory. Generally,…
We consider a constrained shortest path problem with two resources. These two resources can be converted into each other in a particular manner. Our practical application is the energy optimal routing of hybrid vehicles. Due to the…
The actual accelerated expansion of the universe continues being a mystery in physics. Some models had been proposed for this explanations, among them the dark energy, which however has problems of experimental character as well as…
The general covariant Fokker-Planck equations associated with the two different versions of covariant Langevin equation in Part I of this series of work are derived, both lead to the same reduced Fokker-Planck equation for the…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…
Within the theory of General Relativity, we study the solution and range of applicability of the standard geodesic deviation equation in highly symmetric spacetimes. In the Schwarzschild spacetime, the solution is used to model satellite…
We explore a theory of large-scale gravitational quantization, using the general relativistic Hamilton-Jacobi equation to create quantization conditions via a new scalar wave equation dependent upon the total mass and the total vector…
I present the junction conditions for F(R) theories of gravity and their implications: the generalized Israel conditions and equations. These junction conditions are necessary to construct global models of stars, galaxies, etc., where a…
The paper considers existence results of solution for a linear coupled system of Boltzmann transport equations and related inverse problem. The system models the evolution of three species of particles, photons, electrons and positrons.…
In this exclusive study of the modified $f(Q)$ theory of gravity in the open and closed type Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe model, we impose some constraints from the classical energy conditions. The viable range of…
In this paper we study the relativistic Boltzmann equation in a spatially flat FLRW spacetime. We consider Israel particles, which are the relativistic counterpart of the Maxwellian particles, and obtain global-in-time existence and the…
We survey the landscape of $f(R)$ theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of…
We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the…
The purpose of this article is to introduce and study a relativistic motion whose acceleration, in proper time, is given by a white noise. We deal with general relativity, and consider more closely the problem of the asymptotic behaviour of…
We present a purely algebraic formulation (i.e. polynomial equations only) of the minimum-cost multi-impulse orbit transfer problem without time constraints, while keeping all the variables with a precise physical meaning. We apply general…
The purpose of this note is to introduce and study a relativistic motion whose acceleration, in proper time, is given by a white noise. We begin with the flat case of special relativity, continue with the case of general relativity, and…