The Nature of Inertia Explained Using the Field Theory

Analysis of free fall and acceleration of the mass on the Earth shows that using abstract entities such as absolute space or inertial space to explain mass dynamics leads to the violation of the principle of action and reaction. Many scientists including Newton, Mach, and Einstein recognized that inertial force has no reaction that originates on mass. Einstein calls the lack of reaction to the inertial force a serious criticism of the space-time continuum concept. Presented is the hypothesis that the inertial force develops in an interaction of two masses via the force field. The inertial force created by such a field has reaction force. The dynamic gravitational field predicted is strong enough to be detected in the laboratory. This article describes the laboratory experiment which can prove or disprove the hypothesis of the dynamic gravitational field. The inertial force, calculated using the equation for the dynamic gravitational field, agrees with the behavior of inertial force observed in the experiments on the Earth. The movement of the planets in our solar system calculated using that equation is the same as that calculated using Newton’s method. The space properties calculated by the candidate equation explain the aberration of light and the results of light propagation experiments. The dynamic gravitational field can explain the discrepancy between the observed velocity of stars in the galaxy and those predicted by Newton’s theory of gravitation without the need for the dark matter hypothesis.

Teleparallel equivalent theory of (1+1)-dimensional gravity

A theory of （1＋1）-dimensional gravity is constructed on the basis of the teleparallel equivalent of general relativity. The fundamental field variables are the tetrad fields ei^μ and the gravity is attributed to the torsion. A dilatonic spherically symmetric exact solution of the gravitational field equations characterized by two parameters M and Q is derived. The energy associated with this solution is calculated using the two-dimensional gravitational energy- momentum formula.

Formation and Evolution of Wakes in the Spacetime Generated by a Cosmic String in <i>f</i>(<i>R</i>) Theory of Gravity

The formation and evolution of cosmic string wakes in the framework of a f(R) theory of gravity are investigated in this work. We consider a simple model in which baryonic matter flows past a cosmic string. We treat this problem in the Zel’dovich approximation. We compare our results with previous results obtained in the context of General Relativity and Scalar-Theories of Gravity.

f(T) modified teleparallel gravity as an alternative for holographic and new agegraphic dark energy models

In the present work, we reconstruct different f（T）-gravity models corre- sponding to the original and entropy-corrected versions of the holographic and new agegraphic dark energy models. We also obtain the equation of state parameters of the corresponding f（T）-gravity models. We conclude that the original holographic and new agegraphic f （T）-gravity models behave like the phantom or quintessence model, whereas in the entropy-corrected models, the equation of state parameter can justify the transition from the quintessence state to the phantom regime as indicated by the recent observations.

Coseismic gravity and displacement changes of Japan Tohoku earthquake(Mw 9.0)

The greatest earthquake in the modern history of Japan and probably the fourth greatest in the last 100 years in the world occurred on March 11, 2011 off the Pacific coast of Tohoku.Large tsunami and ground motions caused severe damage in wide areas, particularly many towns along the Pacific coast. So far, gravity change caused by such a great earthquake has been reported for the 1964 Alaska and the 2010 Maule events. However, the spatial-temporal resolution of the gravity data for these cases is insufficient to depict a co-seismic gravity field variation in a spatial scale of a plate subduction zone. Here, we report an unequivocal co-seismic gravity change over the Japanese Island, obtained from a hybrid gravity observation（combined absolute and relative gravity measurements）. The time interval of the observation before and after the earthquake is within 1 year at almost all the observed sites, including 13 absolute and 16 relative measurement sites, which deduced tectonic and environmental contributions to the gravity change. The observed gravity agrees well with the result calculated by a dislocation theory based on a self-gravitating and layered spherical earth model. In this computation, a co-seismic slip distribution is determined by an inversion of Global Positioning System（GPS） data. Of particular interest is that the observed gravity change in some area is negative where a remarkable subsidence is observed by GPS, which can not be explained by simple vertical movement of the crust. This indicated that the mass redistribution in the underground affects the gravity change. This result supports the result that Gravity Recovery and Climate Experiment（GRACE） satellites detected a crustal dilatation due to the 2004 Sumatra earthquake by the terrestrial observation with a higher spatial and temporal resolution.

Gravitational constant in f(R) theories of gravity with non-minimal coupling between matter and geometry

We study the effect of the non-minimal coupling between matter and geometry on the gravitational constant in the context of f(R) theories of gravity on cosmic scales. For a class of f(R) models,the result shows that the value of the gravitational constant not only changes over time but also has the dampened oscillation behavior.Compared with the result of the standard ACDM model, the consequence suggests that the coupling between matter and geometry should be weak.

The Many Faces of Gravity

We show that the number of different gravitational effects is significantly greater than previously thought. First of all, it turned out that the observed constancy of the speed of light relative to the surrounding masses is a special case of a previously unknown fundamental gravitational effect related to the action of gravitation on the speed of light. In other words, the constancy of the speed of light becomes an integral part of gravitation. Moreover, it turned out that the increase in inertial mass and the dilation of the proper time of particles that were accelerated relative to the surrounding masses are also consequences of this fundamental gravitational effect. All of these secondary effects are in the same row with such well-known effects as gravitational refraction and gravitational lensing, which are also a consequence of the action of gravitation on the speed of light. Their belonging to gravitation causes a number of unique features, for example, asymmetry in time dilation and anisotropy of the speed of light, which have been successfully confirmed experimentally. The research is based on a detailed analysis of a large set of experimental data using the classical axiomatic approach.

Recent advances of computing coseismic deformations in theory and applications

This paper reviews the recent advances in computing coseismic deformations,and their contributions to seismology and geodesy. At first,an overview on the history of the dislocation theory development is given in the introduction section. Then,emphasis are given on some new developments through few examples in the following sections,such as the new dislocation theory for a 3D Earth model,a new computing scheme on coseismic deflection change of vertical,the relation of dislocation Love number and the conventional Love numbers,the application of dislocation theory applied in satellite gravity observations,the coseismic deformations observed by GRACE,and a new method to determine dislocation Love numbers by GRACE. Furthermore,some advanced theoretical and cases studies are introduced to illustrate how dislocation theory is important in interpret geodetic data,or invert seismic slip for co- and post-seismic processes,using seismic and geodetic data. Final remarks are given in the last section,with discussions,conclusions,comments on existing problems,and expected methods to solve them.

Adapted Metrics for a Modified Coulomb/Newton’s Potential

Modified Theories of Gravity include spin dependence in General Relativity, to account for additional sources of gravity instead of dark matter/energy approach. The spin-spin interaction is already included in the effective nuclear force potential, and theoretical considerations and experimental evidence hint to the hypothesis that Gravity originates from such an interaction, under an averaging process over spin directions. This invites to continue the line of theory initiated by Einstein and Cartan, based on tetrads and spin effects modeled by connections with torsion. As a first step in this direction, the article considers a new modified Coulomb/Newton Law accounting for the spin-spin interaction. The physical potential is geometrized through specific affine connections and specific semi-Riemannian metrics, canonically associated to it, acting on a manifold or at the level of its tangent bundle. Freely falling particles in these “toy Universes” are determined, showing an interesting behavior and unexpected patterns.

Quantum Physics Has a New, and Remarkable, Expansion

Canonical quantization has taught us great things. A common example is that of the harmonic oscillator, which is like swinging a ball on a string back and forth. However, the half-harmonic oscillator blocks the ball at the bottom and then it quickly bounces backwards. This second model cannot be correctly solved using canonical quantization. Now, there is an expansion of quantization, called affine quantization, that can correctly solve the half-harmonic oscillator, and offers correct solutions to a grand collection of other problems, which even reaches to field theory and gravity. This paper has been designed to introduce affine quantization: what it is, and what it can do.

The Primordial Principle of Self-Interaction

The Standard Model of Particle Physics treats four fields—the gravitational, electromagnetic, weak and strong fields. These fields are assumed to converge to a single field at the big bang, but the theory has failed to produce this convergence. Our theory proposes one primordial field and analyzes the evolution of this field. The key assumption is that only the primordial field exists—if any change is to occur, it must be based upon self-interaction, as there is nothing other than the field itself to interact with. This can be formalized as the Principle of Self-interaction and the consequences explored. I show that this leads to the linearized Einstein field equations and discuss the key ontological implications of the theory.

Charged black holes in the infinite derivative theory of gravity

The infinite derivative theory of gravity is a generalization of Einstein gravity with many interesting properties,but the black hole solutions in this theory are still not fully understood.In the paper,we concentrate on studying the charged black holes in such a theory.Adding the electromagnetic field part to the effective action,we show how the black hole solutions around the Reissner-Nordstrom metric can be solved perturbatively and iteratively.We further calculate the corresponding temperature,entropy and electrostatic potential of the black holes and verify the first law of thermodynamics.

On the Gravitational Waves of the Planets Closest to the Earth and Experimental Possible of Its Measurement

The laws of gravity are important for understanding the foundations of the material world at all its levels, from elementary particles to the entire Universe. Therefore, their study allows you to better understand the problems of natural science for all levels of the material world. The greatest opportunities for studying the laws of gravity are associated with the solar system, where the masses of space objects and the laws of their motion are well known. However, the determination of their fields on the basis of traditional theories of gravity still leads to abstract equations that do not give concrete results;therefore, they have a level of hypotheses. A number of initial scientific propositions based on abstract mathematical dependencies have controversial meanings. In particular, schemes of the gravitational interaction of the fields of 2 physical bodies belong to them. Elimination of this disadvantage is the main goal of the work performed. Its main difference and scientific novelty is the substantiation of the spatial wave system of the gravitational interaction of fields on the example of the Sun, the Earth and the planets closest to it, as well as the possibility of testing this system during experimental measurements. The solution to this problem is an urgent and important scientific and applied problem since it develops knowledge about the gravitational field and the material world in general. The performed work is based on the methods of deduction and induction in the research of the material world based on the application of the well-known reliable laws of physics and the general principles of the development of the theory of knowledge. Other research methods are still unknown since the work performed is associated with new scientific discoveries, the search for which is difficult to formalize by technique methods. The results of the study consist in the analysis of secondary waves on the based structural diagram of the superposition of primary gravitational waves between two objects such as the Earth and the Moon, which made it possible to reveal the trail of the shock wave cone behind the orbit of the Moon’s motion. A similar picture can be obtained for the Sun-Venus pair. In this case, the shock wave cone arising behind the orbit of the motion of Venus can intersect the orbit of the Earth’s motion in 2 places: at the entrance to the cone and at the exit from it. It is possible to register a burst of gravitational waves from this cone using the LIGO, VIRGO, KAGRA observatories. Conclusions: To carry out the experiment, it is necessary to perform calculations of the cone of the shock wave of Venus when it moves around the Sun and the position of the points of entry of the Earth into and out of this cone. The solution to this problem is possible in modern conditions with joint work of physicists and astronomers.

Gauge Formulation of Heaviside’s Equations

A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.

Gedanken Experiment (Thought Experiment) about Gravo-Electric and Gravo-Magnetic Fields, and the Link to Gravitons and Gravitational Waves in the Early Universe

Our Gedanken experiment is a thought experiment as to what is called gravo-electric and gravo- magnetic potentials linked to gravo-electric and gravo-magnetic fields. We examine what Padma- nabhan presented in an exercise as of a linkage of electromagnetic fields with Gravitation. The modifications we bring up take the nonrelativistic approximation as the beginning of an order of magnitude estimate as to gravitons, generated electromagnetic fields, and are by definition linked to the total angular momentum of an initial configuration of “particles” of space-time import. The innovation put into Padmanbhan’/s calculation is to for total mass M, used, to substitute in M ~ N(gravitons) times m(g), where m(g) is about 10^?62 grams, as well as specify distances, for the object spinning as being about Planck length in size, give or take a few orders of magnitude. The results are by definition very crude, and do not take into account relativistic effects, but are pro- bably within an order of magnitude important comparison. We conclude with an a comment as to the possibility of an additional polarization as due to a response function of an interferometer to “scalar” polarization as maybe indicate a scalar-tensor gravitational theory as a replacement for General Relativity.

Geometrical Models of the Locally Anisotropic Space-Time

Along with the construction of non-Lorentz-invariant effective field theories, recent studies which are based on geometric models of Finsler space-time become more and more popular. In this respect, the Finslerian approach to the problem of Lorentz symmetry violation is characterized by the fact that the violation of Lorentz symmetry is not accompanied by a violation of relativistic symmetry. That means, in particular, that preservation of relativistic symmetry can be considered as a rigorous criterion of the viability for any non-Lorentz-invariant effective field theory. Although this paper has a review character, it contains (with few exceptions) only those results on Finsler extensions of relativity theory, that were obtained by the authors.

Physical aspects of f(R,G_(μν)T^(μν))modified gravity theories

The paper extends basic Einstein–Hilbert action by incorporating an invariant derived from a specific contraction between the Einstein tensor and energy momentum tensor.This represents a non–minimal coupling between the space–time geometry and matter fields.The fundamental Einstein–Hilbert action is extended by considering a generic function f(R,GμνTμν).This function is subsequently dissected into its primary components:a geometric part reliant on the scalar curvature,and another segment encapsulating the interaction between geometry and matter fields.Distinct cosmological models are formulated at the backdrop of these dynamics,rooted in specific associations between the matter energy-momentum tensor and Einstein tensor.Upon deriving the consequent field equations,the cosmological model's physical implications are explored through a dynamical system analysis applied to diverse coupling functions.This exploration reveals that the current model aligns with various phases in the Universe's evolution,potentially elucidating several late-time historical epochs.

f(R,L(X))-gravity in the context of dark energy with power law expansion and energy conditions

The objective of this work is to generate a general formalism of f(R,L(X))-gravity in the context of dark energy under the framework of K-essence emergent geometry with the Dirac-Born-Infeld(DBI) variety of action,where R is the familiar Ricci scalar,L(X) is the DBI type non-canonical Lagrangian with X=1/2g^(μν)▽_(μ)φ▽_(ν)φ,and φ is the K-essence scalar field.The emergent gravity metric(G_(μν)) and the well known gravitational metric(g^(μν))are not conformally equivalent.We have constructed a modified field equation using the metric formalism in f(R,L(X))-gravity incorporating the corresponding Friedmann equations into the framework of the background gravitational metric,which is of Friedmann-Lemaitre-Robertson-Walker(FLRW) type.The solution of the modified Friedmann equations have been deduced for the specific choice of f(R,L(X)),which is of Starobinsky-type,using the power law expansion method.The consistency of the model with the accelerating phase of the universe has been shown when we restrict ourselves to consider the value of the dark energy density as φ^(2)=8/9=0.888 <1,which indicates that the present universe is dark-energy dominated.Graphical plots for the energy density(ρ),pressure(p),and equation of state parameter(ω) with respect to(w.r.t.) time(t) based on parametric values are interestingly consistent with the dark energy domination theory,and hence the accelerating features.We also highlight the corresponding energy conditions and constraints of the f(R,L(X)) theory with a basic example.

Comprehensive analysis of relativistic embedded class-I exponential compact spheres in f(R,φ)gravity via Karmarkar condition

In this article,we use the prominent Karmarkar condition to investigate some novel features of astronomical objects in the f(R,φ)gravity;R andφrepresent the Ricci curvature and the scalar field,respectively.It is worth noting that we classify the exclusive set of modified field equations using the exponential type model of the f(R,φ)theory of gravity f(R,φ)=φ(R+α(eβR-1)).We show the embedded class-I approach via a static,spherically symmetric spacetime with an anisotropic distribution.To accomplish our objective,we use a particular interpretation of metric potential(grr)that has already been given in the literature and then presume the Karmarkar condition to derive the second metric potential.We employ distinct compact stars to determine the values of unknown parameters emerging in metric potentials.To ensure the viability and consistency of our exponential model,we execute distinct physical evolutions,i.e.the graphical structure of energy density and pressure evolution,mass function,adiabatic index,stability,equilibrium,and energy conditions.Our investigation reveals that the observed anisotropic findings are physically appropriate and have the highest level of precision.

The Nature of Inertial and Vacuum Gravitational Field

The uniformly accelerated motion is studied in the framework of gauge theory of gravity. It is found that, when an inertial reference system is transformed into a uniformly accelerated system by a local gravitational gauge transformation, a non-trivial gravitational gauge field appears. If there is a mass point in the new reference frame, there will be a non-trivial gravitational force acting on it. The nature and the characteristic of this new force are completely the same as those of the traditional inertial force. This new gravitational force is considered to be the inertial force. Therefore, the nature of inertial force is gravity, which is the basic idea of the equi-valence principle.