Related papers: The rocket problem in general relativity
The problem of explaining the acceleration of the expansion of the universe and the observational and theoretical difficulties associated with dark matter and dark energy are discussed. The possibility that Einstein gravity does not…
The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space enables to…
The turbulent jets are usually described by classical velocities. The relativistic case can be treated starting from the conservation of the relativistic momentum. The two key assumptions which allow to obtain a simple expression for the…
We consider f(R) modified gravity theories for describing varying speed of light in a spatially flat FRW model, and find some exact solutions. Also we examine the dynamics of this model by dynamical system method assuming a LambdaCDM…
This work shows that a class of astrodynamics problems subject to mission constraints can be efficiently solved using the Theory of Functional Connections (TFC) mathematical framework by a specific change of coordinates. In these problems,…
Some problems relevant to the relativistic generalization of Maxwell's velocity distribution are discussed.
In this paper, we examined the viability bounds of a higher derivative $f(R,\Box R, T)$ theory through analyzing energy conditions (where $R$ and $T$ are the Ricci scalar and trace of energy momentum tensor, respectively). We take flat…
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr\"odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a well-known model for superfluid quantum…
A new model to describe the dynamics of particles undergoing diffusion in general relativity is proposed. The evolution of the particle system is described by a Fokker-Planck equation without friction on the tangent bundle of spacetime. It…
Optimization of low-thrust trajectories that involve a larger number of orbit revolutions is considered a challenging problem. This paper describes a high-precision symplectic method and optimization techniques to solve the minimum-energy…
A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes photon rockets accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so…
We generalise the Buchdahl-Bondi limit for the case of static, spherically symmetric, relativistic compact stars immersed in Schwarzschild vacuum in f(R)-theory of gravity, subject to very generic regularity, thermodynamic stability and…
This article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized…
In the Wheeler-DeWitt framework, by a gauge fixing procedure, we set up a scheme to recover a Schr\"odinger type equation, living in the orbits space with the {\it lapse} function as evolution parameter. By means of the associated…
The Lambert problem is to determine the gravitational orbit between two points that has a specified time of flight, allowing the second point to be a moving target such as a satellite. After a review of gravitational orbits, a solution of…
Special relativity theory is generalized to two or more ``maximal'' signalling speeds. This framework is discussed in three contexts: (i) as a scenario for superluminal signalling and motion, (ii) as the possibility of two or more ``light''…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
We construct a general relativistic model for the accretion flow of a rotating finite cloud of non-interacting particles infalling onto a Schwarzschild black hole. The streamlines start at a spherical shell, where boundary conditions are…
In this methodological note we discuss several topics related to interpretation of some basic cosmological principles. We demonstrate that one of the key points is the usage of synchronous reference frames. The Friedmann-Robertson-Walker…
The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…