Related papers: The rocket problem in general relativity
The effective equation of state of normal matter is changed in theories where the size of the compact space depends upon the local energy density. In particular we show how the dilution of a fluid due to the expansion of the universe can be…
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…
We study the optimal transport problem in the Euclidean space where the cost function is given by the value function associated with a Linear Quadratic minimization problem. Under appropriate assumptions, we generalize Brenier's Theorem…
Analytical computations in relativistic cosmology can be split into two sets: time evolution relating the initial conditions to the observer's light-cone and light propagation to obtain observables. Cosmological perturbation theory in the…
We present a short introduction to the M{\o}ller gravity theory and study the Schwarzschild solution and self-consistent spontaneous compactification solutions in Kaluza-Klein theories, which can be obtained in the framework of this…
We discuss the modified gravity which may produce the current cosmic aceleration of the universe and eliminates the need for dark energy. It is shown that such models where the action quickly grows with the decrease of the curvature define…
The classical fuel-optimal two-impulse rendezvous problem between Keplerian orbits is revisited from a family-based perspective. Conventional approaches often yield isolated optimal solutions whose mutual relationships remain unclear; yet,…
Low-thrust trajectory design relies heavily on repeated evaluations of fuel consumption and transfer feasibility, which require expensive optimal control solutions. In this work, we show these quantities can be accurately approximated by…
The problem of finding the optimal thrust profile of a launcher upper stage is analyzed. The engine is assumed to be continuously thrusting, following either a linear or a bilevel parametric profile, until reaching the targeted coplanar…
We investigate the application of fractional calculus to model stellar dynamics, focusing on Resonant Relaxation (RR) near a supermassive black hole (SMBH). Standard theories use the local Fokker-Planck (FP) equation, restricted to Gaussian…
A detailed consideration of the Klein-Gordon equation in relativistic quantum mechanics is presented in order to offer more clarity than many standard approaches. The equation is frequently employed in the research literature, even though…
We investigate cosmological solutions of f(R,T) modified theories of gravity for perfect fluid in spatially FLRW metric through phase space analysis, where R is Ricci scalar and T denotes the trace of energy-momentum tensor of matter…
It is shown with several concrete examples that the Dyer-Roeder approximation is valid in spacetimes which fulfill the condition that fluctuations in the expansion rate along a light ray locally cancels with the shear contribution to the…
In this paper we present a new approach to solve the fuel-efficient powered descent guidance problem on large planetary bodies with no atmosphere (e.g. the Moon or Mars) using the recently developed Theory of Functional Connections. The…
This thesis explores the late-time cosmic acceleration within the framework of $f(R,T)$ gravity, a general relativity modification that incorporates the Ricci scalar $R$ and the trace of the energy-momentum tensor $T$. Motivated by…
We generalize Israel's formalism to cover singular shells embedded in a non-vacuum Universe. That is, we deduce the relativistic equation of motion for a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker spacetime.…
Gateway will represent a primary logistic infrastructure in cislunar space. The identification of efficient orbit transfers capable of connecting Earth, Moon, and Gateway paves the way for enabling refurbishment, servicing, and utilization…
We consider the diffeomorphism invariant gravity coupled with the ideal fluid in the non-standard way. The Lorentz-invariance of the graviton propagator in such a theory considered as perturbation over flat background turns out to be broken…
In 1994, Miguel Alcubierre proposed that the well-known special relativistic limitation that particles cannot travel with velocities higher than light speed can be bypassed when such trips are considered globally within specific general…
This paper deals with the impulsive formation control of spacecraft in the presence of constraints on the position vector and time. Determining a set of path constraints can increase the safety and reliability in an impulsive relative…