相关论文: Hooke's memorandum on the development of orbital d…
We live at a time of contradictory messages about how successfully we understand gravity. General Relativity seems to work very well in the Earth's immediate neighborhood, but arguments abound that it needs modification at very small and/or…
Einstein general theory of relativity (GTR) accounted well for the precession of the perihelion of planets and binary pulsars. While the ordinary Newton law of gravitation failed, a generalized version yields similar results. We have shown…
We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and…
Inertia has long been treated as the paradigm of natural motion. This paper challenges this identification through the lens of General Relativity. Drawing on Norton (2012)'s distinction between idealisation and approximation and analysing…
I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing…
In Minkowski spacetime, we consider an isolated system made of two pointlike bodies interacting at a distance, in the nonradiative approximation. Our framework is the covariant and a priori Hamiltonian formalism of "predictive relativistic…
The extension of Dirac's LNH to cover cosmological and fine-structure time-varying "constants", and the rotation of the Universe, is here analysed, including a "derivation" of the angular speed of the present Universe, and of the…
This paper consists of a translation of Andre Tacquet's discussion of the question of sizes of stars in a heliocentric universe, as published in his posthumous Opera Mathematica of 1668, along with introductory material and analysis. While…
A complete model of the universe needs at least three parts: (1) a complete set of physical variables and dynamical laws for them, (2) the correct solution of the dynamical laws, and (3) the connection with conscious experience. In quantum…
Experimental verification of the theoretical predictions made by Albert Einstein in his paper, published in 1905, on the molecular mechanisms of Brownian motion established the existence of atoms. In the last 100 years discoveries of many…
This expository paper relates the Hole Argument in general relativity (GR) to the well-known theorem of Choquet-Bruhat and Geroch (1969) on the existence and uniqueness of globally hyperbolic solutions to the Einstein field equations. Like…
Cosmology is a field of physics in which the use of General Relativity theory is indispensable. However, a cosmology based on Newtonian gravity theory for gravity is possible in certain circumstances. The applicability of Newtonian theory…
The exact solution of the Hamiltonian constraint in canonical gravity and the resultant reduction of Einstein's theory reveal the synergy between gravitation and the intrinsic cosmic clock of our expanding universe. Intrinsic Time…
This review presents a comprehensive overview of Myrzakulov gravity, highlighting key developments and significant results shaping the theory. It examines the foundational principles, field equations, and the role of non-metricity and…
Variational techniques have been used in applications of hydrodynamics in special cases but an action that is general enough to deal with both potential flows and solid-body flows, such as cylindrical Couette flow and rotating planets, has…
We point out serious shortcomings of a very recent article (Iorio in Astrophys. Space Sci. 364:126, 2019) wrongly claiming that the current precision with which we know orbits of planets in the Solar System rules out the possibility of…
Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…
We study the motion of test particles in the gravitational field of a rotating and deformed object within the framework of the adiabatic theory. For this purpose, the Hartle-Thorne metric written in harmonic coordinates is employed in the…
We derive the first-order orbital equation employing a complex variable formalism. We then examine Newton's theorem on precessing orbits and apply it to the perihelion shift of an elliptic orbit in general relativity. It is found that…
The geometric foundations of General Relativity are revisited, with particular attention to its gauge invariance, as a key to understanding the true nature of spacetime. Beyond the common image of spacetime as a deformable 'fabric' filling…