Related papers: Kepler's laws with introduction to differential ca…
We discuss some outstanding open questions regarding the validity and uniqueness of the standard second order Newton-Einstein classical gravitational theory. On the observational side we discuss the degree to which the realm of validity of…
We revisit the Keplerian-like parametrization of the two-body problem in Yukawa gravity studied in the literature. Some inconsistencies, which spoil Bertrand's theorem, observed in the $\eta$ parametrization of the true anomaly $\theta$ and…
Newton's second law may be used to obtain a wave equation, which reduces to Schrodinger's equation in the nonrelativistic limit and for a conservative force.
Previous work established a universal form for the equation of motion of small bodies in theories of a metric and other tensor fields that have second-order field equations following from a covariant Lagrangian in four spacetime dimensions.…
The Earth itself is not stationary but keeps revolving, and its motion further satisfies the law of equal area according to the heliocentric doctrine. That satisfaction can be used to construct the mathematical relationships between the…
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential $V(r)=k r^{\epsilon}$. For zero total energy we show that the…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
Inspired by amazing result obtained by Semay \cite{semay-1}, this study revisits generalised Kepler's third law of an n-body system from the perspective of dimension analysis. To be compatible with Semay's quantum n-body result, this letter…
The dynamics of extended bodies is a fundamental problem in any gravitational theory. In the case of General Relativity, this problem is under study since the theory was published. Several methods have been developed and different…
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
Three decades ago, Ted Jacobson surprised us with a very appealing approach to classical gravity. According to him, the gravitational field equations are the consequence of the first law of thermodynamics applied to a Rindler observer.…
The idea of possible modification to gravity theory, whether it is in the Newtonian or general relativistic premises, is there for quite sometime. Based on it, astrophysical and cosmological problems are targeted to solve. But none of the…
Kepler's orbits with corrections due to Special Relativity are explored using the Lagrangian formalism. A very simple model includes only relativistic kinetic energy by defining a Lagrangian that is consistent with both the relativistic…
In the framework of Einstein's General Relativity Theory and of the Relativistic Theory of Gravitation, the equations governing the trajectories of charged particles in the field created by a charged mass point are given. An analysis of the…
Einstein's equations in matter are gravitational analogues of Maxwell's equations in matter, providing an effective classical description of gravitational fields. We derive Einstein's equations in matter for relativistic fluids, and use…
We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from the Newton's law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly…
The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the…
A classical two dimensional theory of gravity which has a number of interesting features (including a Newtonian limit, black holes and gravitational collapse) is quantized using conformal field theoretic techniques. The critical dimension…
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity…
We study a system of two pointlike particles coupled to three dimensional Einstein gravity. The reduced phase space can be considered as a deformed version of the phase space of two special-relativistic point particles in the centre of mass…