In this paper, the model of the new agegraphic is considered as an alternative to the teleparallel MODIFIED GRAVITY model. First, we obtain the Friedman equations by taking dark matter and dark energy based on the existence of the bulk viscosity in the flat Friedmann– Robertson– Walker metric. So, we obtain the cosmological parameters and the function f(T) by using the power law of the scale factor and the correspondence between the agegraphic model and teleparallel GRAVITY. By plotting the variety of the dark energy equation of state versus the redshift parameter, we describe the accelerated expansion of the universe. Finally, we investigate the stability condition by using the function of sound speed, finding the energy-weak constraints for free parameters.

Considering an action in MODIFIED GRAVITY, the static spherically symmetric solutions in vacuum are investigated. Introducing the Lagrangian multipliers α , we obtained the Lagrangian and equations of motion. For the constant Gauss-Bonnet invariant, the metric leads to de sitter solutions with and. Then for a large class of these models we obtain the exact solutions. Finally we study the thermodynamical quantities of these solutions. we obtain two type solutions for these models. The first case leads to Schwarzschild-de Sitter (anti de Sitter) solution and the other one, results in a new metric. The layout of the paper is the following. The action of GRAVITY is considered and the field quations are derived, then the effect of MODIFIED GRAVITY is considered as an effective stress-energy tensor. For the static spherically symmetric metric and using the method of Lagrangian multipliers to obtain the lagrangian and equations of motion is discussed. Then, the static spherically symmetric vacuum solutions for a large class of these metrics are investigated and the exact solutions are obtained.

In this paper, we study a restricted MODIFIED GRAVITY in which diffeomorphism symmetry is broken. We investigate the astrophysical implications of the model by using the corresponding gravitational potential. By using the weight function of the weak lensing, for the model, the deviation of the model with respect to model has been studied for the late-time cosmology.

In this work, the charged black hole solution to the Brans– Dicke GRAVITY theory in the presence of the nonlinear electrodynamicshas been investigated. To simplify the field equations, a conformal transformation has been introduced whichtransforms the Brans– Dicke– Born– Infeld Lagrangian to that of Einstein-dilaton– Born– Infeld theory. A new class ofð n þ 1Þ-dimensional black hole solution has been constructed out as the exact solution to the Brans– Dicke theory in thepresence of the Born– Infeld nonlinear electrodynamics. The physical properties of the solutions have been studied. Theblack hole charge and temperature have been calculated making use of the Gauss’ s law and the concept of surface GRAVITY, respectively. Also, the black hole mass and entropy have been obtained from geometrical methods. Trough a Smarr-typemass formula as a function of the black hole charge and entropy the black hole temperature and electric potential, as theintensive parameters conjugate to the black hole entropy and charge, have been calculated. The consistency of results of thegeometrical and thermodynamical approaches confirms the validity of the first law of black hole thermodynamics for thisnew black hole solution. Finally, making use of the ensemble canonical method, the local stability or phase transition of thenew ð n þ 1Þ-dimensional Brans– Dicke– Born– Infeld black hole solution has been analyzed.

In this paper, we introduce uberGRAVITY based on the idea of the ensemble average theory of f (R) GRAVITY models. This model has interesting properties including its universality. Another property of this model is its curvature dependency: In high curvatures, uberGRAVITY is reduced to standard Einstein-Hilbert action, while in low curvatures, it vanishes. This transition happens at a scale of R0. It is possible to show that this dimensionful scale plays the role of the cosmological constant at late times. To consider the behavior of the non-linear structure formation, we need to start with the spherical collapse; hence, here we study the spherically symmetric solutions. We show that the radius dependency of these solutions is totally different from the Schwarzchild solution. Interestingly, the solutions looks like the Reissner-Nordstrom in the absence of any electrical charge.

The purpose of this paper is to consider the ring systems in the context of a MODIFIED GRAVITY theory. In fact, the gravitational stability of a ring system consisted of N particle with the same mass m rotating around a massive object at the center is studied. After finding the equation of motion and considering the dynamics of the system in the equilibrium state, perturbative analysis is used in order to find the linearized version of the equations of motion. Finally using the Fourier analysis, the dispersion relation of the system is derived. At the end, using the observational values of the free parameters of the above mentioned theory and also the dispersion equation the stability criterion of the system for several cases is derived. Finally, the results have been compared with the corresponding results in Newtonian GRAVITY.

The field equation following the non-linear Lagrangian -2L + R + aR2 has been considered as an alternative to Einstein's theory. Based on the background field method, the linearized fourth order field equation has been obtained in both the 4-dimensional de Sitter space-time and the flat 5-dimensional ambient space notations. The field equation has been projected into the Minkowskian 4-dimensional space by taking the zero curvature limit. It has been shown that the field equation transforms according to one of the unitary irreducible representations of de Sitter group denoted by P 2,2±, in discreet series.

GRAVITY and its usage in GRAVITY interpretation is still a challenging field. It is not easy to compute these gradients especially in the case of noisy data. Analytical signal is one of the new methods that uses GRAVITY gradients to locate the perturbing body. This method had already been used for high-resolution magnetic and GRAVITY data and rarely used for low-quality GRAVITY data. The GRAVITY gradients and analytical signal have been applied in two different areas, Zahedan where we are looking for Choromite anomalies and Tehran (Mard Abad) where we are investigating for low density anomaly, Probably hydrocarbon.

A great deal of attention has been paid to quantitative interpretation in recent years Two methods, namely the analytic signal an4 the Euler deconvolution (EULDPH) were discussed in this paper. After a short review on the mathematical bases of the methods. two field examples were used to examine the efficiency and limits of the methods when they are applied on a complex geology structure. These methods have already been applied to synthetic models and high - resolution data such as gradiometeric or microGRAVITY data. Noisy GRAVITY data especially in areas of complex geology has rarely been used by these methods and the field examples are exceptions. The low- resolution GRAVITY data was used to provide with residual anomalies. GRAVITY gradients were generated ftom the residual anomaly values. Then applying the GRAVITY gradients to the analytic signal and EULDPH methods. we determine the coordinates of a perturbing body in the field of data. Two field examples, one in the west of Tehran (Mardabad) and another in the southwest of Iran are considered. In the first field we were to determine the location of a hydrocarbon density anomaly. In the second field, we were to determine a Choromit anomaly.