From the hypotheses compatible with microphysics **theory**, this paper establishes a new theoreti- cal model of static universal **gravitation** and deduces new formula of the **theory** of universal gra- vitation. In a first order approximation, the new formula shows the inverse-square law consistent with Newton formula, which would indicate that the new **theory** is consistent with the experimen- tal results that can be reasonably explained by the current **theory** of **gravitation**. The parameters and higher order terms among the coefficients of this paper reveal the numerous infinitesimal neglected effects by current **theory** and experiments. In the first order approximation, the mean- ings of the physical parameters included in coefficients are analyzed and the infinitesimal neg- lected effects are applied in the study of the stability of the universe, which overcomes the diffi- culty of singularity in the cosmology of Newton, Einstein, etc., and concludes that the boundary of universe is unlimited, without any need of the hypothesis that the universe starts off with the big bang. Therefore, this paper establishes a harmonious and ingenious relationship between micro- physics and macrophysics theories. In addition, through the analysis of the formula derived from the **theory** of this paper, it is found that: in general, the gravitational constant is not always a con- stant in the **gravitation** formula requiring high precision; from the perspective of the interaction of field quantum, the acting force may not be equal to counter-acting force under the interaction of indirect contact; the gravity process is an exothermic process; in the gravitational process, anni- hilation effects may exist amongst gravitons; reciprocal translation may exist amongst fundamen- tal forces.

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THE GRAVITATIONAL FIELD OF A BODY WITH ROTATIONAL SYMMETRY IN EINSTEIN'S THEORY OF GRAVITATION ABSTRACT Einstein's set of field equations in vaccuo is reduced to such a form tbat simp~e [r]

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It is obvious that the reader will quickly and easily perceive any new scientific **theory** not from a monograph, but from an article published in a readable scien- tific journal. Gravitational interaction of celestial bodies is a very mysterious phenomenon . It is traditionally attributed (without any further explanation) to the action of forces of “universal **gravitation**”. But where are the threads, the ropes, the chains or the springs that pull celestial bodies one to the other? How does the Earth “know” that it needs to revolve around the Sun? How does it “feel” where the Sun is located? As far as we know there exists no material connection between celestial bodies. But if there is no material connection, does it not mean that gravitational interactions are not a manifestation of the action of forces, but a manifestation of the existence of some heretofore overlooked agent or me- chanism? The Jefimenko’s generalized **theory** of **gravitation** answers this ques- tion with perfect clarity.

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(a) A basic requirement of a geometric **theory** of **gravitation** and elec- trodynamics: Since **gravitation** and electromagnetism are universal long-range interactions, they are expected to be mediated by massless particles. In the latter case, these particles are photons, which are also anticipated from the quantization of electromagnetic radiation predicted by Maxwell’s equations. In the same vein then, one prediction of a quantum **theory** of gravity would be that the interaction would be mediated by the virtual exchange of some massless particles usually called gravitons, which were also predicted by Einstein on the basis of GR [2]. Also, let us recall that in the Lagrangian **theory** of a relativistic field, the trace of the field tensor is expected to be proportional to the square of the mass of the particle. This is then in a perfect agreement with the vanishing trace of the electromagnetic field tensor F µν in order to possess the massless mediator - the photon. In the same

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Bali and Meena [27] have derived conformally flat tilted Bianchi type V cosmological models filled with perfect fluid and conduction. Tilted Bianchi type I cosmological model for perfect fluid distribution in the presence of magnetic field discussed by Bali and Sharma [28]. Pradhan and Rai [29] have evaluated conformally flat tilted Bianchi type V cosmological models filled with disordered radiation in the presence of a bulk viscous fluid and heat flow. Pawar and Dagwal [30-32] have investigated Conformally flat tilted cosmological models, tilted Kantowski-Sachs cosmological models with disordered radiation in scalar tensor **theory** of **gravitation** proposed by Saez and Ballester and tilted Kasner-type cosmological model in B-D **theory**.

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The significance of the present work deals with the modification of gravitational and geometrical aspects of Einstein’s equations. These are 1) scale invariant **theory** of **gravitation** which describes the interaction between matter and **gravitation** in scale free manner; and 2) the gauge transformation, which represents a change of units of measurements and hence gives a general scaling of physical system. The nature of the cosmological model with modified gravity that would reproduce the kinemat- ical history and evolution of perturbation of the universe is investigated.

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About the λ-parameters, it should be mentioned that this property that the λ’s are dynamic parameters as- sumed to be related to the gravitating body in question is the novelty of the ASTG-model. Putting weight to what we already have said, in a way, the dynamism of the λ-parameters makes the ASTG-model a new classical **theory** of **gravitation** where the spin of the gravitating mass enters the gravitational podium. Further, of the λ-parameters, for all conditions of existence, it is assumed that ( λ ≡ 0 ) whenever spin is dropped and what this all means is that with the spin switched off, the ASTG-model reduces to the traditional Newtonian gravita- tional **theory** that we are used to know.

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Newton’s **theory** does not include inductive phenomena, but a relativistic **theory** of **gravitation** should include them. Indeed, under the relativistic mass-energy equivalence, not only the mass is a source of gravitational field but any kind of energy also is. Therefore, a body creates gravitational field not only by mass but also by their kinetic energy, i.e. by their movement. And this, ultimately, is what it means induction: the production of forces by moving bodies [6].

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Abstract:- In this paper, we have investigated spatially homogeneous anisotropic Axially Symmetric universe filled with two minimally interacting fields, matter and holographic dark energy components in Brans-Dicke **theory** of **gravitation**. Exact solutions of field equations are obtained using the fact that scalar expansion is proportional to the shear scalar and constant deceleration parameter. Some physical and kinematical properties of the model are also discussed.

General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A classical **theory** of **gravitation** in flat space-time also avoids the singularity under natural conditions on the density parameters. The uni- verse contracts to a positive minimum and then it expands during all times. It is not symmetric with regard to its mini- mum implying a finite age measured with proper time of the universe. The space of the universe is flat and the total energy is conserved. Under the assumption that the sum of the density parameters is a little bit bigger than one the uni- verse is very hot in early times. Later on, the cosmological model agrees with the one of general relativity. A new inter- pretation of a non-expanding universe may be given by virtue of flat space-time **theory** of **gravitation**.

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In this paper we have obtained the exact solution of the strange quark matter coupled with string cloud in the frame work of Kaluza- Klein **theory** of **gravitation**. In the first part of the paper we have obtained the solution for strange quark matter for (n = 1) which was ignored by Yilmaz (2006) by assuming G H and H 2 . It is observed that the scale factor a and b both are exponential functions of t and energy density is always positive. It is also observed that from Eq. (38) and (39) we get

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In the last few decades, alternative theories to Einstein’s **theory** of **gravitation** have developed mainly scalar tensor theories proposed by Brans and Dicke [51], Nordtvedt [52], Wagoner [53], Ross [54], Dun [55], Saez and Ballester [56], Barber [57] and La & Steinhardt [58]. Among them Brans-Dicke and Saez-Ballester theories are considered to be viable alternatives to general relativity. Brans-Dicke **theory** includes a long range scalar field interacting equally with all forms of matter (with the exception of electromagnetism) while in Saez-Ballester **theory**, metric is coupled with a dimensionless scalar field in a simple manner. This coupling gives satisfactory description of weak fields. This **theory** suggests a possible way to solve the missing-matter problem in non-flat FRW cosmologies. In earlier literature, cosmological models in Saez-Ballester **theory** of **gravitation** have been studied by Singh and Agrawal [59], Shri Ram and Tiwari [60], Singh and Shri Ram [61]. In recent years, Reddy and Naidu [62], Adhav et al. [63], Katore et al. [64] Pradhan and Singh [65] are some of the authors who have obtained the solutions in Saez-Ballester **theory** in different contexts.

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Bianchi type space-times play a vital role in understand- ing and description of the early stages of evolution of the universe. In particular, the study of Bianchi type-II, VIII & IX universes are important because familiar solutions like FRW universe with positive curvature, the desitter universe, the Taub-Nut solutions etc correspond of Bi- anchi type-II, VIII & IX space-times. In view of the im- portance of Bianchi type-II, VIII & IX space- times and also since exact solutions offer an alternative and com- plementary approach to study various cosmological models, in this paper we have presented Bianchi type-II, VIII & IX perfect fluid cosmological models in Brans- Dicke **theory** of **gravitation**.

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Viewing gravitational energy-momentum as equal by observation, but different in essence from inertial energy- momentum naturally leads to the gauge **theory** of volume-preserving diffeomorphisms of an inner Minkowski space which can describe **gravitation** at the classical level. This **theory** is quantized in the path integral formalism starting with a non-covariant Hamiltonian formulation with unconstrained canonical field variables and a manifestly positive Hamiltonian. The relevant path integral measure and weight are then brought into a Lorentz- and gauge- covariant form allowing to express correlation functions—applying the De Witt-Faddeev-Popov approach—in any meaningful gauge. Next the Feynman rules are developed and the quantum effective action at one loop in a background field approach is renormalized which results in an asymptotically free **theory** without presence of other fields and in a **theory** without asymptotic freedom including the Standard Model (SM) fields. Finally the BRST apparatus is developed as preparation for the renormalizability proof to all orders and a sketch of this proof is given.

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A revolutionary development seems to have taken place in cosmology during the last few years. The latest development of super-string **theory** and super gravitational **theory** have created interest among scientists to consider higher dimensional space time, for study of the early universe. A number of authors Zeldovich (1980), Sahdev (1984), Emelynor et. al. (1986), Chatterjee and Bhui (1990, 1993) have studied physics of the universe in higher dimensional space time. Overduin and Wesson (1987) have presented an excellent review of higher dimensional unified theories, in which the cosmological and astrophysical

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Synge has referred to Mach's p rin cip le and the Equivalence p rin c ip le as "a p air of decaying and dangerous ru in s." Whether or not this is an ov erstatement, the relationship of Mach's p rin cip le to general r e l a tiv it y is" s t i l l a subject fo r debate. Although Einstein was led towards his formulation of general r e l a tiv it y as a resu lt o f Mach's ideas, his view was u ltim at ely quite d iffe re n t from th at of Mach: th at the world is understandable e n tire ly in terms of geometry, which exists before any physical experiment is ca rried out. He cam e to rega rd a ll attempts to represent m atter in the **theory** as unsatis factory and, in order to free i t from any p a rtic u la r choice of m atter tensor, de alt e v entu ally only with the g ra v ita tio n a l equations of free spac e.^

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Abstract: In this paper, we study a class of solution of Saez-Ballester scalar tensor **theory** with barotropic fluid and bulk viscous fluid for the new class of Bianchi model. We consider two cases of an interacting and non-interacting two fluid and obtained general results. The exact solution of the field equations are obtained for three different form of scale factor. The Physical and geometrical aspects of the models are discussed.

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In the year 1979, I have studied a **theory** of **gravitation** in flat space-time (GFST) which gives for weak gravitational fields the same results as GR to mea- surable accuracy. The energy-momentum of **gravitation** of GFST is a tensor in How to cite this paper: Petry, W. (2019)

In this paper, it is proved that the small deformation strain tensor can be used instead the funda- mental metric tensor of the General **Theory** of Relativity, in order to formulate a Dynamic **Theory** of **Gravitation**. Also, a solution of the velocity of the gravitational interactions is given in terms of the escape velocity due to the apparent size of the heavenly bodies. This last paragraph is the motiva- tion and the importance of the study here presented. Thus, when it has a couple of celestial bodies separated by a distance in space, its apparent sizes as seemed at a distance plays a special role in the gravitational interactions. This is so because of some effect over the size due to the very big distances in space. In that situation, the values of their escape velocities are dependent on their mass, and critically on their apparent radius. It is proved that they are the medium used by the gravity to transmit its effects like propagating force of nature. Then, when the escape velocities meets in some point of the space between the bodies, they pull each other; because they are the carriers of the respective attractive gravitational fields. In other words, the escape velocity due to the apparent size is the exchanging coin in the gravitational interactions. Also it is proposed that such a dynamic process is the responsible for the strong link which is established between any couple of interacting heavenly objects in the Universe.

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Understanding the nature of mass is crucial in fundamental re- search. Since attempts to detect the Higgs boson, and therefore to verify the Higgs field as the mass-generating mechanism of the Stan- dard Model, have been unsuccessful, paper proposes a very simple model of **gravitation** that use the Descartes’ void (holes in space- time). The advantage of the present approach is that it can easily explain the curvature of space-time using the properties of Descartes’ vacuum only. **Gravitation** is a phenomenon by which all objects with mass attract each other. Hole **theory** of **gravitation** explains why ob- ject have mass, how all objects with mass attract each other. Matter interacts with space-time that and radiates a flux of holes that is the cause of the **gravitation**. Thus for explanation of **gravitation** the present **theory** use the hole structure of space-time only.

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