scholarly journals THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR ‘FREE FALL’: A DIALECTICAL REASSESSMENT OF KEPLER’S LAWS:

2017 ◽  
Vol 13 (4) ◽  
pp. 4876-4880
Author(s):  
Abdul Malek
Keyword(s):  
General Relativity ◽  
Albert Einstein ◽  
Universal Gravitation ◽  
Dialectical Approach ◽  
Superluminal Velocity ◽  
Theories Of Gravity ◽  
Third Law ◽  
The Law ◽  
Free Falling

The concept of Universal Gravitation or “Free Fall” common to both Newton’s Law and the Theory of General Relativity (GR) of Albert Einstein is one-sided, idealistic and an anti-dialectical notion in cosmology. It is also in violation of the successful principle of Newton’s Third Law of “equal and opposite reaction” and the impossibility of the existence of a single isolated force in terrestrial mechanics. This conceptual defect of the theories of gravity as universal attraction leads to superluminal velocity of free falling mass points, cosmic paradoxes, singularities, “Black Holes”, “dark matter” and other cosmic mysteries. A reassessment of Kepler’s laws and a dialectical approach to astrophysics in particular and to cosmology in general, is proposed.

scholarly journals A new approach to the derivation of the law of universal gravitation from Kepler’s laws

2021 ◽  
Vol 2081 (1) ◽  
pp. 012012
Author(s):  
P N Antonyuk
Keyword(s):  
Universal Gravitation ◽  
New Approach ◽  
Inverse Square Law ◽  
Kepler's Laws ◽  
Third Law ◽  
The Law ◽  
Kepler’S Laws

Abstract Everyone knows that the inverse square law follows from Kepler’s third law. Let us prove more: the law of universal gravitation follows from Kepler’s third law.

Conservation laws

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Dynamical System ◽  
Angular Momentum ◽  
Conservation Laws ◽  
Total Energy ◽  
Superposition Principle ◽  
Momentum Conservation ◽  
Conserved Quantities ◽  
Angular Momentum Conservation ◽  
Third Law ◽  
The Law

This chapter defines the conserved quantities associated with an isolated dynamical system, that is, the quantities which remain constant during the motion of the system. The law of momentum conservation follows directly from Newton’s third law. The superposition principle for forces allows Newton’s law of motion for a body Pa acted on by other bodies Pa′ in an inertial Cartesian frame S. The law of angular momentum conservation holds if the forces acting on the elements of the system depend only on the separation of the elements. Finally, the conservation of total energy requires in addition that the forces be derivable from a potential.

scholarly journals Breaking the cosmological background degeneracy by two-fluid perturbations in f(R) gravity

2015 ◽  
Vol 24 (07) ◽  
pp. 1550053 ◽  
Author(s):  
Amare Abebe
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Structure Formation ◽  
Background Level ◽  
Cosmological Perturbations ◽  
Gauge Invariant ◽  
First Order ◽  
Cosmological Background ◽  
Theories Of Gravity ◽  
Two Fluid

One of the exact solutions of f(R) theories of gravity in the presence of different forms of matter exactly mimics the ΛCDM solution of general relativity (GR) at the background level. In this work we study the evolution of scalar cosmological perturbations in the covariant and gauge-invariant formalism and show that although the background in such a model is indistinguishable from the standard ΛCDM cosmology, this degeneracy is broken at the level of first-order perturbations. This is done by predicting different rates of structure formation in ΛCDM and the f(R) model both in the complete and quasi-static regimes.

scholarly journals CAN f(R) GRAVITY MIMIC GENERAL RELATIVITY?

2012 ◽  
Vol 10 ◽  
pp. 63-68 ◽  
Author(s):  
JE-AN GU
Keyword(s):  
General Relativity ◽  
Differential Equations ◽  
Early Time ◽  
Einstein Equations ◽  
Modified Theories Of Gravity ◽  
Cosmological Perturbations ◽  
Long Run ◽  
Theories Of Gravity ◽  
The Stability ◽  
Higher Order Differential Equations

We discuss the stability of the general-relativity (GR) limit in modified theories of gravity, particularly the f(R) theory. The problem of approximating the higher-order differential equations in modified gravity with the Einstein equations (2nd-order differential equations) in GR is elaborated. We demonstrate this problem with a heuristic example involving a simple ordinary differential equation. With this example we further present the iteration method that may serve as a better approximation for solving the equation, meanwhile providing a criterion for assessing the validity of the approximation. We then discuss our previous numerical analyses of the early-time evolution of the cosmological perturbations in f(R) gravity, following the similar ideas demonstrated by the heuristic example. The results of the analyses indicated the possible instability of the GR limit that might make the GR approximation inaccurate in describing the evolution of the cosmological perturbations in the long run.

scholarly journals The radiation instability in modified gravity

2021 ◽  
Vol 36 (08n09) ◽  
pp. 2150060
Author(s):  
Spiros Cotsakis ◽  
Dimitrios Trachilis
Keyword(s):  
General Relativity ◽  
General Solution ◽  
Modified Gravity ◽  
Evolution Equations ◽  
Formal Series ◽  
Series Expansions ◽  
General Polynomial ◽  
Theories Of Gravity ◽  
Polynomial Extensions

We study the problem of the instability of inhomogeneous radiation universes in quadratic Lagrangian theories of gravity written as a system of evolution equations with constraints. We construct formal series expansions and show that the resulting solutions have a smaller number of arbitrary functions than that required in a general solution. These results continue to hold for more general polynomial extensions of general relativity.

scholarly journals Quantum interference in external gravitational fields beyond General Relativity

2021 ◽  
Vol 81 (10) ◽  
Author(s):  
Luca Buoninfante ◽  
Gaetano Lambiase ◽  
Luciano Petruzziello
Keyword(s):  
General Relativity ◽  
Quantum Interference ◽  
Relativistic Effects ◽  
Newtonian Potential ◽  
Alternative Theories Of Gravity ◽  
Gravitational Fields ◽  
Decoherence Rate ◽  
Relativistic Regime ◽  
Theories Of Gravity ◽  
To Come

AbstractIn this paper, we study the phenomenon of quantum interference in the presence of external gravitational fields described by alternative theories of gravity. We analyze both non-relativistic and relativistic effects induced by the underlying curved background on a superposed quantum system. In the non-relativistic regime, it is possible to come across a gravitational counterpart of the Bohm–Aharonov effect, which results in a phase shift proportional to the derivative of the modified Newtonian potential. On the other hand, beyond the Newtonian approximation, the relativistic nature of gravity plays a crucial rôle. Indeed, the existence of a gravitational time dilation between the two arms of the interferometer causes a loss of coherence that is in principle observable in quantum interference patterns. We work in the context of generalized quadratic theories of gravity to compare their physical predictions with the analogous outcomes in general relativity. In so doing, we show that the decoherence rate strongly depends on the gravitational model under investigation, which means that this approach turns out to be a promising test bench to probe and discriminate among all the extensions of Einstein’s theory in future experiments.

scholarly journals Testing the Vainshtein mechanism using stars and galaxies

2015 ◽  
Vol 24 (12) ◽  
pp. 1544021 ◽  
Author(s):  
Jeremy Sakstein ◽  
Kazuya Koyama
Keyword(s):  
General Relativity ◽  
Solar System ◽  
Main Sequence ◽  
Alternative Theories Of Gravity ◽  
The Novel ◽  
Main Sequence Stars ◽  
Cosmic Expansion ◽  
Astrophysical Objects ◽  
Theories Of Gravity ◽  
Alternative Theories

The Vainshtein mechanism is of paramount importance in many alternative theories of gravity. It hides deviations from general relativity (GR) in the solar system while allowing them to drive the acceleration of the cosmic expansion. Recently, a class of theories have emerged where the mechanism is broken inside astrophysical objects. In this essay, we look for novel probes of these theories by deriving the modified properties of stars and galaxies. We show that main-sequence stars are colder, less luminous and more ephemeral than GR predicts. Furthermore, the circular velocities of objects orbiting inside galaxies are slower and the lensing of light is weaker. We discuss the prospects for testing these theories using the novel phenomena presented here in light of current astrophysical surveys.

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