Relativistic Theory Of Gravitation Research Articles

One-Dimensional Relativistic Self-Gravitating Systems.

One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here, I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature of the absence of gravitational radiation, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the two-body, three-body, four-body, and N-body problems. Quite general exact solutions can be obtained for the two-body problem, unlike the situation in general relativity in three spatial dimensions for which only highly specified solutions exist. The three-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For N≥4, other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems.

A Causal Net approach to Relativistic Quantum Mechanics and Gravitation

In this paper we discuss a causal network model to describe quantum mechanics and gravittation, where space–time is built solely from point events and connecting probabilities. A causal net provides a representation which combines the quantum complementary features of both partticles and waves as each vertex on the causal net represents a possible point event or particle observation. Simultaneity on the causal net is defined by hyperplanes of equivalent proper time. The causal net model when constructed in Minkowksi space–time is shown to lead to a formulation for relativistic quantum mechanics including the Dirac equation. In a curved Riemann space–time the causal paths of the causal net are geodesics and in the local Lorentz frame the net probabilities and the Dirac formalism are preserved. The variation of space–time density of events in the causal paths modifies the metric and provides a space–time curvature leading to the Hilbert action associated with general relativity. Consideration of the Schwarzchild metric shows that in classical limit the perturbation in the density of possible events is proportional to the Newtonian gravitational potential.

The Convincing Cosmic Energy Gravitational Genesis of the Strongest Geomagnatic Anomalies of the Magnetic Field of the Earth

The author presents convincing evidence of the cosmic (planetary and solar) energy gravitational origin (related to the maximal and minimal combined planetary and solar integral energy gravitational influences on the internal rigid core of the Earth) of the maximal temporal intensifications of the global magnetic processes of the Earth. In fairly good agreement with the calculated date 2007.416666666 AD (of the local minimal planetary and solar integral energy gravitational influence on the internal rigid core), it was observed the very rapid changes of the geomagnetic field near the date March 2007 AD (corresponding approximately to 19-20 April 2007 AD). This fairly good agreement gives the additional convincing argument that the date March 2007 AD can be considered as the possible beginning of the geomagnetic reversal during the evaluated range (2007÷2216) AD. The strong magnetic anomaly occurred on 6 January 2020 AD in perfect agreement with the calculated date 2020.016666667 AD (corresponding to 6 January 2020 AD) related to the local maximal planetary and solar integral energy gravitational influence on the internal rigid core. In fairly good agreement with the calculated date 2023.26666666 AD (corresponding approximately to 7 April 2023 AD) of the local maximal planetary and solar integral energy gravitational influence on the internal rigid core, it was observed the strongest (during the last 6 years) magnetic anomaly on 23 March 2023 AD. These convincing agreements demonstrate the physical validity of the established global prediction thermohydrogravidynamic principles, which can be considered as the proven physical basis for the development of the general unified geophysical theory (describing the possible geomagnetic reversal during the evaluated range (2007 ÷ 2216) AD) combining the Special Theory of Relativity, the relativistic electrodynamics and the relativistic theory of the non-stationary gravitation, which can be developed based on the established physical analogy between the established relation for the energy flux (of the gravitational energy) and the Lorentz’s calibration condition (for the vector potential related with the scalar potential of the non-stationary electromagnetic field).

Traversable wormhole model with massive gravitons, two fluids, and a variable gravity

We construct a new cosmological model based on relativistic theory of gravity characterized by massive gravitons. The new Friedmann–Robertson–Walker model is characterized by the presence of a static traversable wormhole, massive gravitons, and a variable gravitational coupling constant. To recover the Bianchi identity, a second cosmic fluid is introduced in the theory. Motivated from cosmic dark radiation phenomenological arguments, which suggest that the dynamical component of dark energy could be dominated by a bath of dark radiation, we assume that the original cosmic fluid is radiative, whereas the new cosmic fluid is phantom. The total equation of state of our model is equal to −1. The new model is characterized by an effective Hubble parameter. The solutions of the dynamical equations reveal an accelerated universe with a scale factor of hyperbolic type which allows the deceleration parameter to change sign from a decelerating phase to an accelerating phase. We have evaluated the deceleration parameter, the jerk and the present day variations of the gravitational constant which agree with astronomical observations.

On the Theories of Gravitation Developed Based on the Ideas of Galileo and Descartes

As it’s known, the results of the relativistic theory of gravitation were developed by Einstein, which were based on the ideas of Galileo's principle of relativity. On the other hand, it should be noted that Descartes developed a more general approach to the foundation of the theory of knowledge, leading to the derivation of Hamilton's equation. Subsequently, the fundamental equations of the Hamilton-Jacobi-Schrödinger theory (HJS) were obtained by solving them for a multitude of bodies (particles) subject to constraints, and Gibbs' equations for the case when par-ticles move chaotically. In the article, the author attempts to demonstrate the possibilities of in-terpreting the nature of the HJS equations as a basis for developing a new variant of the theory of gravitation.

Teoría relativista de gravitación para la dinámica Newtoniana modificada

Modified Newtonian dynamics (MOND) is a hypothesis that proposes a modification of Newton's law of universal gravitation to account for observed properties of galaxies. This theory is an alternative to the hypothesis of dark matter in terms of explaining why galaxies do not appear to obey the currently understood laws of physics. In this work, we present a relativistic theory of gravitation for MOND.

Gravitoelectromagnetic Field Strength Tensor in Flat Spacetime Frame: Dynamics of a Gyroscope in the Earth’s Gravitational Field

In this article, we develop gravitoelectromagnetism (GEM) as a formal relativistic theory of gravitation characterized by a field potential fourvector in a flat (Minkowski) spacetime frame. By reorganizing the Lense-Thirring spacetime metric of linearized general relativity, we have determined the appropriate field potential four-vector and the field strength tensor which generates dynamics in the GEM field. The general covariant equation of motion of the spin four-vector of a gyroscope driven by the GEM field strength tensor provides the expected form of the frame-dragging and geodetic effects after introducing a gyromagnetic ratio η = 4 as an internal dynamical property of the gyroscope.

A viable relativistic scalar theory of gravitation

We build a self-consistent relativistic scalar theory of gravitation on a flat Minkowski spacetime from a general field Lagrangian. It is shown that, for parameters that satisfy the equivalence principle, this theory predicts the same outcome as general relativity (GR) for every classical solar-system test. This theory also admits gravitational waves that propagate at the speed of light, and the gravitational radiation energy loss in a binary system is shown to be very similar to the GR prediction. We then analyze the strong gravity regime of the theory for a spherically symmetric configuration and find that there is an effective ‘singularity’ near the Schwarzschild radius. The main goal of this work is to show that, contrary to what is commonly believed, there are relativistic scalar theories of gravitation defined on a Minkowski spacetime that are not ruled out by the classical solar system tests of GR.

Limits of Relativist Process Engineering: Current Feasibility in the International Space Station (ISS)

Many authors have published in the field of relativistic fluid mechanics (Von LAUE, 1911) (HALBWACHS, 1960) (PICHON, 1965) (LICHNEROWICZ, 1966) (BRUHAT, 1966) (MARLE, 1969) (ARZELIES, 1971) (MAHJOUB, 1971) (REZZOLLA et al., 2013) (DISVONZI, 2014) (DERRADI et al., 2016). However, the demonstrations carried out are subject to caution, either due to errors, or by the use of the BOLTZMANN equation or the principle of least action associated with the Lagrangian (FONTEIX et al., 2020). The conference presented at the previous SFGP congress (CAMARGO et al., 2019) was based on the results of a publication (FONTEIX et al., 2020). The aim was to write the energy, momentum and matter balances in special relativity, for continuous fluid mixtures (ARZELIES, 1971). Contrary to custom, these assessments were demonstrated using 2 principles. The first is well known, it is the inseparability of space and time during a change of inertial frame (MINKOWSKI, 1907). The second is our original proposal: in the Tangent Inertial Frame of a flat space-time, the equations of the relativistic dynamics of continuous fluid mixtures and those of classical physics are identical. Thanks to this, we were able to integrate relativistic gravitation (BRAGINSKY et al., 1992) (Mc DONALD, 1997) (TARTAGLIA et al., 2004) in flat space-time (not curved) and electromagnetism. However, we had not considered nuclear reactions and quantum phenomena (SCHULMAN, 1980), nor approached relativistic thermodynamics (STRUCHTRUP, 1998). We will not do it more here, but we will see in the present conference if it is possible, based on the previous results, to make experiments whose results differ significantly from those carried out on earth, namely experiments carried out in the fastest usable vehicle currently available: the International Space Station (ISS).

The Primordial Particle Accelerator of the Cosmos

In a previous paper we have shown that superluminal particles are allowed by the general relativistic theory of gravity provided that the metric is locally Euclidean. Here we calculate the probability density function of a canonical ensemble of superluminal particles as function of temperature. This is done for both space-times invariant under the Lorentz symmetry group, and for space times invariant under an Euclidean symmetry group. Although only the Lorentzian metric is stable for normal matter density, an Euclidian metric can be created under special gravitational circumstances and persist in a limited region of space-time consisting of the very early universe, which is characterized by extremely high densities and temperatures. Superluminal particles also allow attaining thermodynamic equilibrium at a shorter duration and suggest a rapid expansion of the matter density.

Energy in the relativistic theory of gravity

The more precise definition and the more fundamental understanding of the concepts of time, energy, entropy and information are building upon the new, relativistic foundation of gravity. This lecture is an attempt to explain the basic principles that underpin this progress, by focusing on the simple but subtle universal definition of energy. The principles are unearthed from Einstein’s theory and Noether’s theorems, beneath a century of misconceptions.

Preface

This special issue of the Arabian Journal of Mathematics consists of research articles on some interesting topics in Theoretical & Mathematical Physics as well as theoretical aspects of Relativistic Astrophysics. These research articles were presented in an International Conference on Relativistic Astrophysics and Gravitation (ICRAG) held in Ulugh Beg Astronomical Institute of Uzbekistan during May 12–14, 2021.

General relativistic theory of gravity and electricity

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear throug the geometry. We look for the formally most simple expression for the law of gravitation in the absence of an electromagnetic field, and then the most natural generalization of this law. This theory contain Maxwell theory in first approximation. In the following we outline the scheme of the general theory and then show in which sense this contains the law of the pure gravitational field and Maxwell theory.

A relativistic mass dipole gravitational theory and its connections with AQUAL

It will be shown that a gravitational theory based on there being an additional contribution to the gravitational field from mass dipoles leads to the same field equation that arises from the AQUAL formulation of MOND. However, unlike AQUAL, the mass dipole theory does not require a modification of Newtonian gravitational theory. In addition, both SR and linearized GR field equations will be derived for the mass dipole and AQUAL gravitational theories.

Spectral dynamics of interacting particles: in Brownian motion and gravitating dust solutions

Statistical analysis of the behaviour of interacting particles suspended in a fluid undergoing Brownian motion is extended by a deeper investigation into its spectral properties. By utilizing random matrix theory, spectral statistics is then integrated into the Einstein–Brownian motion formulation for interacting particles suspended in a fluid. The modified version of the conventional Brownian formulation along with the resulting insights are presented in this work. The second part of this work provides the implementation of spectral statistics to a system of interacting massive particles of a gravitating dust solution. Formulating the system on a Riemannian manifold with a random metric tensor, a deterministic dust solution density is achieved, where spectral and statistical aspects of the relativistic theory of gravity are uncovered. Potential application in modeling properties of galaxy formation and evolution is discussed.

New Relativistic Theory for Modified Newtonian Dynamics.

We propose a relativistic gravitational theory leading to modified Newtonian dynamics, a paradigm that explains the observed universal galactic acceleration scale and related phenomenology. We discuss phenomenological requirements leading to its construction and demonstrate its agreement with the observed cosmic microwave background and matter power spectra on linear cosmological scales. We show that its action expanded to second order is free of ghost instabilities and discuss its possible embedding in a more fundamental theory.

Quantum detection of inertial frame dragging

A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by mass-energy currents. These effects have recently been confirmed by classical observations. Here we show, for the first time, that they can be observed by a quantum detector. We study the response function of Unruh De-Witt detectors placed in a slowly rotating shell. We show that the response function picks up the presence of rotation even though the spacetime inside the shell is flat and the detector is locally inertial. The detector can distinguish between the static situation when the shell is non-rotating and the stationary case when the shell rotates and the dragging of inertial frames, i.e. gravitomagnetic effects, arise. Moreover, it can do so when the detector is switched on for a finite time interval within which a light signal cannot travel to the shell and back to convey the presence of rotation.

Beyond Einstein’s General Relativity: Hybrid metric-Palatini gravity and curvature-matter couplings

Einstein’s General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing, at least for weak gravitational fields. Its predictions range from the existence of black holes and gravitational radiation (now confirmed) to the cosmological models. Indeed, a central theme in modern Cosmology is the perplexing fact that the Universe is undergoing an accelerating expansion, which represents a new imbalance in the governing gravitational equations. The cause of the late-time cosmic acceleration remains an open and tantalizing question, and has forced theorists and experimentalists to question whether GR is the correct relativistic theory of gravitation. This has spurred much research in modified theories of gravity, where extensions of the Hilbert–Einstein action describe the gravitational field, in particular, [Formula: see text] gravity, where [Formula: see text] is the curvature scalar. In this review, we perform a detailed theoretical and phenomenological analysis of specific modified theories of gravity and investigate their astrophysical and cosmological applications. We present essentially two largely explored extensions of [Formula: see text] gravity, namely: (i) the hybrid metric-Palatini theory; (ii) and modified gravity with curvature-matter couplings. Relative to the former, it has been established that both metric and Palatini versions of [Formula: see text] gravity possess interesting features but also manifest severe drawbacks. A hybrid combination, containing elements from both of these formalisms, turns out to be very successful in accounting for the observed phenomenology and avoids some drawbacks of the original approaches. Relative to the curvature-matter coupling theories, these offer interesting extensions of [Formula: see text] gravity, where the explicit nonminimal couplings between an arbitrary function of the scalar curvature [Formula: see text] and the Lagrangian density of matter, induces a nonvanishing covariant derivative of the energy-momentum tensor, which implies nongeodesic motion and consequently leads to the appearance of an extra force. We extensively explore both theories in a plethora of applications, namely, the weak-field limit, galactic and extragalactic dynamics, cosmology, stellar-type compact objects, irreversible matter creation processes and the quantum cosmology of a specific curvature-matter coupling theory.

Relativistic Gravitation Based on Symmetry

We present a Relativistic Newtonian Dynamics ( R N D ) for motion of objects in a gravitational field generated by a moving source. As in General Relativity ( G R ), we assume that objects move by a geodesic with respect to some metric, which is defined by the field. This metric is defined on flat lab spacetime and is derived using only symmetry, the fact that the field propagates with the speed of light, and the Newtonian limit. For a field of a single source, the influenced direction of the field at spacetime point x is defined as the direction from x to the to the position of the source at the retarded time. The metric depends only on this direction and the strength of the field at x. We show that for a static source, the R N D metric is of the same form as the Whitehead metric, and the Schwarzschild metric in Eddington–Finkelstein coordinates. Motion predicted under this model passes all classical tests of G R . Moreover, in this model, the total time for a round trip of light is as predicted by G R , but velocities of light and object and time dilation differ from the G R predictions. For example, light rays propagating toward the massive object do not slow down. The new time dilation prediction could be observed by measuring the relativistic redshift for stars near a black hole and for sungrazing comets. Terrestrial experiments to test speed of light predictions and the relativistic redshift are proposed. The R N D model is similar to Whitehead’s gravitation model for a static field, but its proposed extension to the non-static case is different. This extension uses a complex four-potential description of fields propagating with the speed of light.

Extended Relativistic Invariance, Quantization of the Kinetic Momentum

The aim of this research is a better understanding of the quantization in physics. The true origin of the quantization is the existence of the quantized kinetic momentum of electrons, neutrinos, protons and neutrons with the value. It is a consequence of the extended relativistic invariance of the wave of fundamental particles with spin 1/2. This logical link is due to properties of the quantum waves of fermions, which are functions of space-time with value into the and End(Cl3) Lie groups. Space-time is a manifold forming the auto-adjoint part of . The Lagrangian densities are the real parts of the waves. The equivalence between the invariant form and the Dirac form of the wave equation takes the form of Lagrange's equations. The momentum-energy tensor linked by Noether's theorem to the invariance under space-time translations has components which are directly linked to the electromagnetic tensor. The invariance under of the kinetic momentum tensor gives eight vectors. One of these vectors has a time component with value . Resulting aspects of the standard model of quantum physics and of the relativistic theory of gravitation are discussed.