Related papers: The rocket problem in general relativity
The two-body problem in general relativity is reduced to the problem of an effective particle (with an energy-dependent relativistic reduced mass) in an external field. The effective potential is evaluated from the Born diagram of the…
Current spacecraft mass are mostly fuel, this is dictated by the lack of fueling stations in space and also by the Tsiolkovsky rocket equation which defines the mass ratio needed to escape earths gravity. The Tsiolkovsky rocket equation…
Modern astrophysical and cosmological models are plagued with two severe theoretical difficulties, namely, the dark energy and the dark matter problems. Relative to the former, high-precision observational data have confirmed with startling…
The construction of an averaged theory of gravity based on Einstein's General Relativity is very difficult due to the non-linear nature of the gravitational field equations. This problem is further exacerbated by the difficulty in defining…
It has long been known that once you cross the event horizon of a black hole, your destiny lies at the central singularity, irrespective of what you do. Furthermore, your demise will occur in a finite amount of proper time. In this paper,…
Gravitational collapse and bubble evolution in the asymptotical Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe is an intriguing and intricate problem. We systematically analyze dynamics for contact \sch-FLRW (McVittie) spacetimes,…
We derive general relativistic Gaussian equations for osculating elements for orbits under the influence of a perturbing force without any restrictions in an underlying Schwarzschild space-time. Such a formulation provides a way to describe…
An extension of the theory of General Relativity is proposed, based on pseudo-complex space-time coordinates. The new theory corresponds to the introduction of two, in general different, metrics which are connected through specific…
We propose a new generalisation of general relativity which incorporates a variation in both the speed of light in vacuum (c) and the gravitational constant (G) and which is both covariant and Lorentz invariant. We solve the generalised…
We study an optimal transport problem where, at some intermediate time, the mass is accelerated by either an external force field, or self-interacting. We obtain regularity of the velocity potential, intermediate density, and optimal…
Quantum cosmology based on the Wheeler De Witt equation represents a simple way to implement plausible quantum effects in a gravitational setup. In its minisuperspace version wherein one restricts attention to FLRW metrics with a single…
A vast wealth of literature exists on the topic of rocket trajectory optimisation, particularly in the area of interplanetary trajectories due to its relevance today. Studies on optimising interstellar and intergalactic trajectories are…
A solution for the problem of understanding observed rotation curves in galaxies without the introduction of dark matter halos is presented. This solution has been obtained upon considering the distribution of masses in the expanding…
In this methodological paper we consider two problems an astronaut faces with under the black hole horizon in the Schwarzschild metric. 1) How to maximize the survival proper time. 2) How to make a visible part of the outer Universe as…
The works reported in this thesis primarily address the application of the Raychaudhuri equation in two intriguing problems in gravitational physics. These problems still lack universally accepted explanations. The first problem is related…
A new class of exact solutions of Einstein's field equations with a perfect fluid source, variable gravitational coupling $G$ and cosmological term $\Lambda$ for FRW spacetime is obtained by considering variable deceleration parameter…
We study the possibility that in the model introduced in \cite{GBN}, the Gauss-Bonnet term alone gives rise to the cosmic acceleration and super-acceleration in four-dimensional FLRW space-time at the late time. We also discuss transitions…
Einstein's field equations in FRW space-times are coupled to the BGK equation in order to derive the stress energy tensor including dissipative effects up to second order in the thermodynamical forces. The space-time is assumed to be…
This paper presents a simple approach to low-thrust optimal-fuel and optimal-time transfer problems between two elliptic orbits using the Cartesian coordinates system. In this case, an orbit is described by its specific angular momentum and…
This article solves an optimal control problem arising in attitude control of a spacecraft under state and control constraints. We first derive the discrete-time attitude dynamics by employing discrete mechanics. The orientation transfer,…