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In this paper, we study a particular type of inflation by using non-local Friedman equations that are somehow derived from the zero levels of string field theory and express a tachyonic action. Then, we challenge it by further refining de Sitter (dS) swampland conjecture (FRdSSC) monitoring. Therefore, we investigate some quantities, such as potential and Hubble parameters. We also consider slow-roll parameters to examine quantities such as the scalar spectrum index and the tensor-to-scalar ratio. Using straightforward calculations, we investigate this model from the swampland conjecture perspective in terms of the cosmological parameters, i.e., ($n_s$), ($r$), and observable data such as Planck 2018, by constructing some structures such as $(c_1,2-n_s)$ and $(c_1,2-r_s)$. Then, we make a new restriction for this conjecture as $c_12c_22$ and get a limit for this model in the range $c0.0942$. We find this inflationary model is strongly in tension with the dS swampland conjecture (dSSC), i.e., $c_1=c_2 \neq \mathcal{O}(1)$. So, we shall challenge it with the FRdSSC, which has some free parameters, viz., $a,b>0$, $a+b=1$, and $q>2$. By setting these parameters, we examine the compatibility of the mentioned conjecture with this inflationary model. Finally, we infer from this string field inflation model that it satisfies the FRdSSC with the constraint of its free parameters $a$, $b$, and $q$., Comment: 17 pages, 4 figures

Mimetic gravity analysis has been studied as a theory in various types of general relativity extensions, such as mimetic f(R) gravity, mimetic f(R, T) gravity, mimetic f(R, G) gravity, etc., in the literature. This paper presents a set of equations arising from mimetic conditions and studies cosmic inflation with a combination of mimetic f(G) gravity and swampland dS conjectures. We analyze and evaluate these results. Therefore, we first thoroughly introduce the mimetic f(G) gravity and calculate some cosmological parameters such as the scalar spectral index, the tensor-to-scalar ratio, and the slow-roll parameters. Also, we investigate the potential according to the mimetic f(G) gravity. Then we will challenge the swampland dS conjectures with this condition. By expressing the coefficient of swampland dS conjectures viz $C_{1}$ and $C_2$ in terms of $n_{s}$ and $r$, we plot some figures and determine the allowable range for each of these cosmological parameters and these coefficients, and finally, compare these results with observable data such as Planck and BICEP2/Keck array data. We show $C_{1}$ and $C_2$ are not $\mathcal{O}(1)$, so the refining swampland dS conjecture is not satisfied for this inflationary model. Then we examine it with further refining swampland dS conjecture, which has a series of free parameters such as $a,b>0$, $q>2$, and $a+b=1$. By adjusting these parameters, the compatibility of the mentioned conjecture with the inflationary model can be discussed. We determine the further refining swampland dS conjecture is satisfied. when $a < \frac{1}{1.00489}=0.99513$, we can always find $a$, $b$ and $q$ whose value is larger than 2, viz for $q=2.4$, we find $0.99185\leq a < 1$, which we can choose $a=0.99235$ according to the condition $a < 0.99513$. Also we know $b=1-a$, so we will have $1-0.99235=0.00765 > 0$., Comment: 25 pages, 5 figures. Accepted for publication in International Journal of Modern Physics D (This work is dedicated to the memory of Prof Farhad Darabi)

In this paper, we use a Tsallis holographic dark energy model in two forms, interacting and non-interacting cases, to acquire some parameters as the equation of state for the energy density of the Tsallis model in the FRW universe concerning the complex form of quintessence model. We will study the cosmology of complex quintessence by revamping the potential and investigating the scalar field dynamics. Then we analyze ($\omega-\omega'$) and stability in two cases, i.e., non-interacting and interacting. We will explore whether these cases describe a real universe by calculating fractional energy density $\Omega_{D}$ and concerning two parts of the quintessence field effect ( complex and real part ) by considering the real part of this field to be a slow-roll field. We know that the part in which the fractional energy density ($\Omega_{D} > 1$) does not describe a real universe. Also, we specified an interacting coupling parameter $b^{2}$ that depends on the constant parameter of the Tsallis holographic model ($\delta$) with respect to fractional energy density ($0.73$). Unlike independence between the fractional energy density and interacting coupling in the real quintessence model, we determine a relationship among these parameters in this theory. Finally, by plotting some figures, we specify the features of ($\omega-\omega'$) and ($\nu_{s}^{2}$) in two cases and compare the result with each other., Comment: 22 pages, 4 figures, Accepted for publication in Communications in Theoretical Physics

There are two important different mechanisms, the imaginary potential and entropic force, to investigate the dissociation of heavy quarkonia. In this paper, we calculate these two quantities for static and moving quarkonia in the rotating black 3-brane Type IIB supergravity solution dual to N = 4 super Yang-Mills theory on the Coulomb branch (cSYM) at strong coupling. At T 6= 0, there are two black hole branches: the large and small black hole branches. We investigate the effects of rotating parameter and rapidity for the static and moving quakonium at the large and small black hole branches. We find both mechanisms have the same results. In the large black hole branch: as T/{\Lambda} and \b{eta} increase the thermal width decreases and so the suppression becomes stronger. In the small black hole branch: increasing T/{\Lambda} leads to increasing the thermal width and the quarkonium dissociates harder but \b{eta} has an opposite effect., Comment: 15 pages, 7 figures

The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter {\theta} and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases., Comment: 16 pages, 5 figures

In this paper, we investigate the heavy quark potential and the jet quenching parameter in a system with Lifshitz and hyperscaling violation exponents, by using the AdS/CFT correspondence. It is shown that the heavy quark potential and the jet quenching parameter are dependent upon the nonrelativistic parameters. We show how the heavy quark potential changes with the hyperscaling violation parameter {\theta}, dynamical parameter z, temperature T and charge Q. Increasing z and {\theta} lead to increasing and decreasing the potential respectively. The potential decreases and increases by increasing Q and T . It is investigated how the jet quenching parameter changes with the hyperscaling violation parameter {\theta} and dynamical parameter z. Also, we add some electromagnetic field and obtain its effect on the jet quenching parameter and see as z and {\theta} increasing this parameter decreases and the electric and magnetic fields affect differently on that., Comment: 18 pages, 5 figure

In this paper, we calculate the drag force of a charged particle in systems with hyperscaling violation using the AdS/CFT correspondence. We obtain energy loss, friction coefficient, diffusion and quasi normal modes of a heavy point particle. Here, we consider two cases. In the first, we assume the heavy point particle moves with constant velocity v. In the second case, we assume the heavy point particle rotates along a circle of radius L with angular velocity {\omega}. Also, we add some electromagnetic field and obtain the energy loss. Finally, we draw some figures for the drag force with respect to the velocity and the temperature. As well, we show how the drag force and energy loss change with the hyperscaling violation parameter {\theta}, dynamical parameter z, mass m and charge Q., Comment: 21 pages, 4 figures

In this paper, we study a theory of gravity called mimetic $f(R, T)$ in the presence of swampland dS conjecture. For this purpose, we introduce several inflation solutions of the Hubble parameter H(N) from $f(R, T)= R+\delta T$ gravity model, in which R is Ricci scalar, and T denotes the trace of the energy-momentum tensor. Also, $\delta$ and $N$ are the free parameter and a number of e-fold, respectively. Then we calculate quantities such as potential, Lagrange multiplier, slow-roll, and some cosmological parameters such as $n_{s}$ and $r$. Then we challenge the mentioned inflationary model from the swampland dS conjecture. We discuss the stability of the model and investigate the compatibility or incompatibility of this inflationary scenario with the latest Planck observable data., Comment: 34 pages, 7 figures, accepted in Communications in Theoretical Physics

In this paper, we study various cosmological parameters and quantities in scalar-tensor gravity from inflation and swampland conjecture. Therefore, by selecting different models such as power-law, exponential, and logarithmic in the framework of scalar-tensor theory, we obtain potential, tensor-to-scalar ratio, and the scalar spectral index. Next, we examine new constraints and compare the corresponding results with the latest observable data. Here, we take advantage of the obtained results and determine the compatibility or incompatibility of the corresponding model with the swampland conjectures, Comment: 28pages, 16 figures, accepted in MPLA

Wormholes are speculative structures linking disparate space-time points. Their geometry can be obtained by solving Einstein equations with tolerating the violation of null energy conditions. Recently, many researchers have studied different wormholes according to different criteria, and they achieved remarkable results. In this paper, we investigate a series of exact solutions of the static wormhole with smeared mass source geometry in modified $f(R)$ gravity theories. In fact, we consider the Lorentzian density distribution which is coming from a particle-like source. To be more specific, the modified gravity models we consider here are some power laws. We compute resulting solutions according to the wormhole field equations. We also specify parameters such as the radial pressure and transverse pressure as well as various energy conditions such as null energy conditions, weak energy conditions and strong energy conditions. Finally, by plotting some figures, in addition to identifying the wormhole throat, we describe the results of either the violation or the satisfaction of the energy conditions completely., Comment: 27 pages, published in Mod. Phys. Lett. A

Recently researchers have been studying various conditions as swampland criteria in cosmological implications. They have studied many inflation models with different swampland conditions. Occasionally these conjectures are modified and lead to fascinating points. The swampland conjecture is in contradiction with the slow-roll single-field inflation model. So in this paper, we will briefly describe resolving this contradiction with the special method; we consider a small parameter {\lambda} with respect to a coupling function in inflation and resolve this important antithesis. Then we will discuss a new point of view in studying inflation models according to the swampland criteria. Therefore we introduce some inflation models and challenge the swampland criteria. We specify the allowable range of cosmological parameters as the tensor-to-scalar ratio (r) the scalar spectral index (ns) according to the latest observable data. Next, we study the new constraints to determine the compatibility or incompatibility of the corresponding model with the swampland conjectures. Finally, we express the results and compare them with the latest observational data by plotting some figures., Comment: 20 pages, 6 figure, accepted for publication in Astroparticle Physics

In this paper, we focus on the possible correlation between conjectures KSS bound and weak gravity conjecture (WGC). The hydrodynamic values KSS bound and weak gravity conjecture constraint the low-energy effective field theory. These conjectures identify UV complete theories. We give four, six and eight order derivative corrections to corresponding action and employ the hyperscaling violating charged AdS$_{d+2}$ black brane solution. These corrections lead us to find correlation between conjectures KSS bound and weak gravity conjecture. We see that, with increasing perturbation correction, this correlation is more likely to appear. We consider dynamical constant $z=1$, $d=5$ and obtain the range of hyperscaling violation exponent $d+z-2\leq\theta\leq d+z-1$ for the above mentioned black brane. Here, we show that higher derivative corrections reduce the ratio of $\frac{M}{Q}$ to extremal black holes. Likewise, we also obtain the universal relaxation bound $\tau\geq \frac{1}{\pi T}$ and KSS bound $\frac{\eta}{s}\geq \frac{1}{4\pi}$ for our model. The results indicate that there is a possibility of a relationship between the two conjectures. Our studies also show the consistency of the WGC and the KSS bound conjectures for all corrections (except curvature-cubed, $\beta_2$) in the extremal and near-extremal condition., Comment: 27 pages, 10 figures

The universal thermodynamic relations between corrections to entropy and extremality for various black holes solutions have been studied. In this regard, we hereby consider a number of different black brane solutions in different structures for perturbative corrections to general relativity. These are, namely, black brane solution in Rastall AdS massive gravity, Einstein-Yang-Mills AdS black brane solution in massive gravity and general anisotropic black brane in Horava-Lifshitz gravity. We calculate both the entropy and extremality bound by introducing a small constant correction to the action. Remarkably, we find that black brane violates the universal thermodynamic relations. In other words, a universal relation between corrections to entropy and extremality are not valid in the black brane structure., Comment: 14 pages; 2 captioned figures

Over the past few decades, inflation models have been studied by researchers from different perspectives and conditions in order to introduce a model for the expanding universe. In this paper, we introduce a modified $f(R)$ gravitational model as ($R+\gamma R^{p}$) in order to examine a new condition for inflation models. Given that our studies are related to a modified $f(R)$ gravitational model on the brane, therefore we will encounter modified cosmological parameters. So, we first introduce these modified cosmological parameters such as spectral index, a number of e-folds and etc. Then, we apply these conditions to our modified $f(R)$ gravitational model in order to adapt to the swampland criteria. Finally, we determine the range of each of these parameters by plotting some figures and with respect to observable data such as Planck 2018., Comment: 21 pages, 15 captioned figures, Published in Physica Scripta

In this paper, we study the inflationary scenario in logarithmic f(R) gravity, where the rate of inflation roll is constant. On the other hand, our gravitational f(R) model is a polynomial plus a logarithmic term. We take advantage of constant-roll conditions and investigate the cosmic evolution of the logarithmic f(R) gravity. Therefore, we plot some figures such as the scalar spectrum index $n_{s}$ and tensor-to-scaler ratio $r$ concerning $n$, $\beta$ and model's constant parameters, i.e., $\alpha$, $\theta$ and $\gamma$ respectively. Also, we obtain the potential by using the constant roll condition. We know that the potential value obtained with this condition has an exact value. Next, we challenge it with refined swampland conjecture with respect to the Planck data. Finally, we compare our results with the experimental data, especially Planck 2018., Comment: 20pages, 5 figures

In this paper, we study a constant-roll inflationary model in the presence of a noncommutative parameter with a homogeneous scalar field minimally coupled to gravity. The specific noncommutative inflation conditions proposed new consequences. On the other hand, we use anisotropic conditions and find new anisotropic constant-roll solutions with respect to noncommutative parameter. Also, we will plot some figures with respect to the specific values of the corresponding parameter and the swampland criteria which is raised from the exact potential obtained from the constant-roll condition. Finally, different figures lead us to analyze the corresponding results and also show the effect of above mentioned parameter on the inflationary model., Comment: 18 pages, 16 figures. accepted by The European Physical Journal C

Our primary goal in this paper is to confirm new universal relations in black hole thermodynamics. We investigate the universal relations by selecting different black holes. First, we obtain the black holes' thermodynamic relations assuming a new minor correction is added to the AdS part of the action. Then we confirm the universal relations by performing a series of direct calculations. It is noteworthy that according to each of the properties related to black holes, a new universal relation can be obtained according to this method. We confirm two different types of these universal relations for various block holes. Furthermore, we also consider black holes in AdS space surrounded by perfect fluid. We use the small correction to the action and obtain the modified thermodynamic quantities. We achieve two new universal relations which correspond to the parameters of perfect fluid and magnetic charge of the Bardeen AdS Black Hole. Finally, the new universal relation leads us to understand the charge-to-mass ratio, i.e., WGC-like behavior. We also find that the weak gravity conjecture condition is satisfied for the black hole surrounded by perfect fluid., Comment: 28 pages, 4 figures, modified title

In this paper, we study the Penrose process and the maximum energy extracted from the collision of two particles near the Kerr-Newman black hole with WGC condition. We consider the collision process when two particles collide in the ergosphere region of a black hole, scattering two new particles; one of them falls into the black hole and the other escapes to infinity. Our calculations also show an increasing in the energy. We also checked how much energy could be received from a black hole for particles with different spins. Results of this paper will help us to identify and study the black holes of astrophysics and the particles with different spins. Also, it states how black holes work in WGC conditions., Comment: 18 pages, 33 figures

In this paper, we use corrected $f(R)$ gravitational model which is polynomial function with a logarithmic term. In that case, we employ the slow-roll condition and obtain the number of cosmological parameter. This help us to verify the swampland conjectures which is guarantee the validation of low - energy quantum field theory. The obtained results shown that the corresponding model is consistent with the swampland conjectures. Also the upper and lower limit of the parameter \textcolor{red}{$n$} are \textcolor{blue}{0.15} and \textcolor{blue}{0.0033}. Finally, by using scalar spectrum index $ n_{s} $ and tensor to scalar ratio $ r $ relations and compared with Planck 2018 empirical data, we obtain the coefficients $\alpha$,$\beta$ and $\gamma$. Also, the corresponding results are creaked by several figures, literature and also plank 2018 data., Comment: 17 pages. 13 figures

In this paper, we consider the first order correction of the entropy and temperature in a charged black hole with a scalar field. Here, we apply such correction for the different cases of black holes. These corrections are due to the thermal fluctuations of statistical physics. Also, we take advantage of such corrections and study the $ P - V $ critically and phase transition. Also, we investigate the effect of correction on the critical point and stability of the system. We obtain modified thermodynamics quantities and find effects of thermal fluctuations in the stability of the black hole. We find that stability of black hole is depend on the thermal fluctuations. Finally, we compare the results of the corrected and uncorrected by thermodynamical quantities., Comment: 23 pages, 13 figures

In this paper, we consider Klein Gordon particle near Reissner-Nordstr\"{o}m black hole. The symmetry of such background lead us to compare the corresponding Laplace equation with the generalized Heun functions. Such relation help us achieve the generalized $sl(2)$ algebra and some suitable results for describing the above mentioned symmetry. On the other hand in case of $r\rightarrow r_{+}$ which is near the proximity black hole, we obtain the energy spectrum and wave function. When we compare the equation of $R-N$ background with Laguerre differential equation, we show that the obtained energy spectrum is same as three dimensional harmonic oscillator. So, finally we take advantage of harmonic oscillator energy and make suitable partition function. Such function help us to obtain all thermodynamical properties of black hole. Also, the structure of obtained entropy lead us to have some bit and information theory in the $R-N$ black hole., Comment: 12 pages. arXiv admin note: text overlap with arXiv:1001.0785 by other authors

In this paper, we study the thermodynamic properties of Kiselev black hole and its holographic dual. We obtain the thermodynamic product formula for the Kiselev black hole. We consider Kiselev Black hole surrounded by both dust and radiation. We find that the area (or entropy) product formula for both cases is mass-independent as well as the case in the Einstein gravity, which interpreted as universal quantity. Moreover, we calculate the black hole entropy bound for both the inner and outer horizons. Furthermore, we show that the central charges of the left and right moving sectors are not the same via universal thermodynamic relations. Such universal relations lead us to calculate the central charge of conformal field theory (CFT). Finally, we see that the left and right of central charge of CFT are same., Comment: 17 pages, References added in the new version

In this paper, we study $P-V$ criticality of Kerr-Newman $AdS$ black hole with a quintessence field. We calculate critical quantities and show that for the equation state parameter $\omega= -\frac{1}{3}$, the obtained universal ratio ($\frac{P_{c}\upsilon_{c}}{T_{c}}$) is quite same as Kerr-Newman $AdS$ black hole without dark energy parameter. We investigate the influence of quintessence field $\alpha$, equation state parameter $\omega$ and angular momentum $J$ on the efficiency $\eta$. We find that $\eta$ is increased by increasing $J$ and $\alpha$ and decreasing charge $Q$ of black hole. We show when $\omega$ increases from $-1$ to $-\frac{1}{3}$ the efficiency decreases. Also we study ratio $\frac{\eta}{\eta_{C}}$ (which $\eta_{C}$ is the Carnot efficiency) and see that the second law of the thermodynamics is satisfied by special values of $J$ and $\alpha$ and holds for any value of $Q$. We notice that in this case by increasing $\omega$ from $-1$ to $-\frac{1}{3}$ the range of $J$ and $\alpha$ increases., Comment: arXiv admin note: text overlap with arXiv:1710.08642

The entropic force experienced by a moving quarkonia in a plasma, is computed in a hyperscaling violation background by holography approach. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We use the results for HSV parameters which obtained in our paper [1] as appropriate values satisfying condition $ImV_{Q\bar{Q}}< 0$. We will show that, in this background the entropic force of the meson shows a decreasing behaviour corresponds to increasing dissociation length. Results of this paper are in agreement with our mentioned work. In addition we will find diffusion constant in an exact case and by an exact approach [2] which satisfies the mentioned condition in there., Comment: 13 pages, 2 figures. arXiv admin note: text overlap with arXiv:1706.04021

In this paper we employ the Horava-Lifshitz black holes solutions and obtain the corresponding Hamiltonian. It helps us to take new variables and it will be written by harmonic oscillator form. This leads us to apply non-commutative geometry to the new Hamiltonian and obtain the corresponding Lagrangian. And then, we take some information from Finsler geometry and write the Lagrangian of the different kinds of Horava-Lifshitz black holes. We show that the corresponding Lagrangian in non-commutative and Finsler geometry for above mentioned black holes completely coincidence together with some specification of parameters. But in case of rotation, the place of center of mass energy completely different, so the particle goes to inside of black hole rapidly without falling into singularity. So in that case, two Lagrangians cover each other at $0

The unusual asymptotic structure of the accelerating black holes led to ambiguity in their geometric characteristics and thermodynamic behavior. Motivated by the interesting properties of such black holes and the significant role of electric charge and string tension on their structure, we study the thermodynamic behavior of these black holes by two methods and examine the changes of free parameters on the thermal behavior of the black holes. First, we investigate phase transition and thermal stability of the system through the use of heat capacity in the non-extended phase space. We examine the effects of electric charge, string tension and the cosmological constant on the phase transition and stability of the system. We also find that to have a phase transition, we have to apply some constraints on the free parameters. Then, we employ the geometrical thermodynamic (GT) method to study phase transition and compare the obtained results with those of the heat capacity. Next, we work in the extended phase space by considering the cosmological constant as a dynamical pressure and evaluate the existence of van der Waals like phase transition. We obtain critical quantities and study the effective role of electric charge and string tension on these quantities. Finally, we make use of the GT method in the extended phase space and find that the results of the GT method, heat capacity and $P-V$ diagram lead to a consistent conclusion., Comment: 26 pages, 14 figures, accepted for publication in Annals of Physics

The effect of dark energy on the low and high temperature of strip region of the boundary field theory dual to AdS black holes was studied. In this framework, we investigate this behavior for different types of equation state and different regimes of normalization factor (a). We will see that the change of entanglement entropy is growing up with increasing a and |\omega|., Comment: 13 pages, 1 figures

In this paper, we use deformation approach and obtain the corresponding Lagrangian of charged test particle. Also, we show the effect of NC parameters on the Lagrangian of test particle in HL background with charge and without charge. Also, we see in case of $\beta=\theta$ and without charge, the deformed and non-deformed Lagrangian will be same. Also in case of $\beta=\theta$ and with charge will be the same but the charge or field need some scaling. Finally, We show that two theories in case of $\beta\neq\theta$ with charge is completely different. It means that in case of NC geometry in addition to have time components of field we have $r$ and $x_{i}$ components., Comment: 9 pages

In this paper, we calculate thermodynamical quantity of Kerr-Newman-AdS black hole solution in quintessence matter. Then, we show that how the rotation and cosmological parameters effect to the thermodynamics properties of black hole. Also, we investigate both types of phase transition for different values of $\omega$ parameter in extended phase space. We notice that type one of phase transition occurs for $P<0.42$ and $a<0.5$. And also we see that the phase transition point shifts to higher entropy when pressure $P$, rotation parameter $a$ and $\alpha$ increase. Also, we find that by changing parameter $\omega$ from -1 to $-\frac{1}{3}$, the critical point shifts to higher entropy. Then we study type two of phase transition and show critical points increase by increasing parameter $\alpha$. Also, we show that the critical point shifts to higher entropy when $\alpha$, $\omega$ and rotation parameter $a$ decrease. Finally, we find that by decreasing pressure the first critical point shifts to lower entropy and second critical point shifts to higher entropy.

In the present work, we wanted to find the possible way in order to make the equivalence between non-commutative and Finsler geometries as two useful mathematical tools. Based on this purpose, we were concerned to search this possibility by investigating the massive gravity black holes. Firstly the Lagrangian of the system is introduced and then it is rewritten in the non-commutative regime by definition of the new variables. On the other hand, we focus on the Finsler geometry in order to find a Finslerian function which is equivalent to the mentioned non-commutative Lagrangian under special conditions. Also, the effective potential of the system was calculated as a part of the corresponding conditions., Comment: 13 pages

In this study we apply two different methods in the context of $AdS/CFT$ correspondence and calculate the diffusion coefficient and $DC$ conductivity of a four-dimensional spatially anisotropic static black hole. First, the \emph{modified} transport coefficients is obtained by stretched horizon method and Fick's law in the context of the membrane paradigm. In order to do such calculation, we use the Maxwell equations with electromagnetic gauge field propagating in two dimensions. Two dimensional propagating gauge field leads to the complex transport coefficients which is proved by present paper. In second step, we explain electro-thermal method and employ an effective vector field and extract retarded Green's function on the classical boundary. Then, $DC$ conductivity and diffusion coefficient are obtained by using Kubo formula. Our calculation can be applied on two well-known examples of anisotropic black holes as the Einstein-Maxwell-dilaton-axion model and AdS-Einstein-Maxwell-dilaton-axion in massive gravity., Comment: 17 pages

In this paper, we investigate the effects of non-commutative phase-space on the quintom cosmological model. In that case, we discuss $\Lambda_{1}$, $\Lambda_{2}$ and other cosmological parameters and show that they are associated to deformation parameters $\theta$ and $\beta$. Generally one can say that, the non-commutative parameter plays important role in physics and here also help us to arrange the divergency of cosmological constant. We draw time-dependent scale factor and investigate the effect of non-commutative parameters. Finally, we take advantage from non-commutative phase-space and obtain the deformed Lagrangian for the quintom model. In order to discuss some cosmological phenomena as dark energy and inflation, we employ Neother symmetry., Comment: 17 pages, 1 figure. References added in the revised version

In this paper, we take the slowly rotating black three-brane background and perturb it by introducing a vector gauge field. We find the components of the gauge field through Maxwell equations and Bianchi identities. Using currents and some ansatz we find Fick's first law at long wavelength regime. An interesting result for this non-trivial supergravity background is that the diffusion constant on the stretched horizon which emerges from Fick's first law is a complex constant. The pure imaginary part of the diffusion constant appears because the black three-brane has angular momentum. By taking the static limit of the corresponding black brane the well known diffusion constant will be recovered. On the other hand, from the point of view of the Fick's second law, we have the dispersion relation $\omega=-iDq^{2}$ and we found a damping of hydrodynamical flow in the holographically dual theory. Existence of imaginary term in the diffusion constant introduces an oscillating propagation of the gauge field in the dual field theory.

The entropic force and the imaginary part of potential experienced by a moving quarkonia in a plasma, are computed in a charged deformed AdS background by holography approaches. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We show that the charge in deformed AdS background deeply effect on the increasing entropic force and decreasing thermal width. So, the dissociation length of the meson becomes short when charge is increasing. In addition, the entropic force and thermal width are increased by the deformation of the space. Therefore the deformation parameter in such background leads us to find process with arbitrary dissociation length of quark- anti quark., Comment: We found some new results based on which, this work can not be confirmed exactly

In this paper, we introduce Einstein power-law Maxwell-Scalar gravity with Liouvill potential in n + 1 dimension. The corresponding metric background or solution of above mentioned action lead us to achieve some thermodynamics quantities of black hole. On the other hand, we take information from $AdS/CFT$ correspondence and investigate some parameters in $QCD$ as jet quenching and entropic force. We note that two obtained parameters give some important information about $Q\bar{Q}$ moving in $QGP$ media and dissociation length of quark-antiquark. Finally, we have several figures for the jet quenching parameter and entropic force. The corresponding figures show how two parameters are affected by power law Maxwell field with different of $p$.

In this paper, we consider dyonic charged AdS black hole which is holographic dual of a van der Waals fluid. We use logarithmic corrected entropy and study thermodynamics of the black hole and show that holographic picture is still valid. Critical behaviors and stability also discussed. Logarithmic corrections arises due to thermal fluctuations which are important when size of black hole be small. So, thermal fluctuations interpreted as quantum effect. It means that we can see quantum effect of a black hole which is a gravitational system., Comment: 11 pages, 5 figures. References added. Revised according to PRD report

In this paper, we take cosmological constant as a thermodynamical pressure and it's conjugate quantity as a thermodynamical volume. This expression help us to investigate the phase transition and holographic heat engine. So, in order to have Van der Waals fluid behaviour in Horava -Lifshitz (HL) black hole, we modified the solution of such black hole with some cosmology ansatz. Also from holographic heat engine, we obtain Carnot efficiency for the HL black hole. The phase transition of the system lead us to investigate the stability condition for the corresponding black hole. In that case, we show that the stability exist only in special region of black hole., Comment: 18 pages and 12 figures. arXiv admin note: text overlap with arXiv:1205.0146 by other authors

In this paper, we consider a deformed AdS background and study effect of deformation parameter on the pair production rate of the Schwinger effect. The electrostatic potential is important for the pair production in the holographic Schwinger effect. In this paper, we analyze the electrostatic potential in a deformed AdS background and investigate the effect of deformation parameter which may be useful to test of AdS/QCD. In the case of zero temperature we find that larger value of the deformation parameter leads to a smaller value of separation length of the test particles on the probe. Also we find a finite maximum of separation length in presence of modification parameter., Comment: 21 pages, 17 figures. Title changed, references and figures added in the new version

In this paper, we determine thermodynamical quantities for one kind of higher dimensional black holes. We take two charged and neutral blackfold which are higher dimension. We investigate the thermodynamical properties of such black hole at near horizon. By expanding those metrics around horizon, considering periodicity condition of imaginary time and applying some thermodynamical constraints, we extract stress energy tensor of blackfolds. We compare the thermodynamical properties of charged and neutral blackfold. We see here that the stress energy tensor of charged blackfold has brane-tension component in addition to thermal properties. Then by knowing that the spacetime of neutral blackfold is Ricci-flat and there is a nice relation between Ricci-flat and AdS spacetimes we determine the AdS form of Ricci-flat. Also we calculate the corresponding temperature which is satisfied by our previous calculation. Finally, we check the phase transition of blackfolds and show that there is not any critical point for them. So, the thermodynamical stability of both blackfolds will be proven, this result agree with literature., Comment: 11 pages

In this paper, we investigate imaginary part of the potential for a moving quarkonia in plasma. In order to verify the validity of imaginary part of the potential we employ hyperscaling violation metric background. In QCD system the imaginary part of potential shows the decay behaviour and the corresponding potential should be negative. The corresponding potential always appears in QCD as an exponential function. We find general constraints for Im$V_{Q\bar{Q}}$ at the near horizon limit and apply them for some known cases. Finally, we find the suitable spatial dimension d, z and $\theta$ also rapidity $\eta$ for two interesting cases. Our calculation with AdS/CFT guarantees the dynamical parameter as a $\theta$ in hyperscaling violation metric background. We also present the hyperscaling violationg metric in this context very close to YM theory with finite temperature., Comment: 21 pages, 2 figures

We note that, in extended phase space the cosmological constant is a thermodynamic variable. In this paper, this cosmological constant lead us to consider a black hole as a heat engine. So, here we take advantage from holographic heat engine and study two kind of different black holes. We first investigate a static black hole (Dyonic BH) and consider the necessary condition to have high efficiency. Also we continue our investigation for dynamic black hole (rotating charged black hole) and study the effect of rotating parameter on the thermodynamic efficiency of holographic heat engine. We show that the rotating parameter has a more effective role than electric charge in thermodynamic efficiency.

In this paper we consider charged and neutral blackfold and extract the Brown-York stress energy tensor. Also, we show that the neutral blackfold spacetime is Ricci- flat and the other spacetime is not. This Ricci-flat condition gives us opportunity to calculate the AAdS spacetime. In order to have dual theory one can consider the AAdS in Fefferman- Graham coordinates. This frame gives correct form of stress tensor in the boundary. The corresponding tensor with using this frame will be traceless and conserved. Such stress tensor is same as perfect fluid and it proves the dual renormalized theory exists for the neutral blackfold ., Comment: 12 pages

In general we can say that the thermal width of quarkonia corresponds to imaginary part of its potential. Gravity dual of theories give explicit form of potential as $V_{Q\bar{Q}}$ . Since there is an explicit formula for $Im V_{Q\bar{Q}}$ one can consider different gravity duals and study the results of contribution of various parameters. Variable gravity duals of moving pair in plasma have different results for potential. Our paper shows that deformation parameter c in warp factor leads to new results that we present them for arbitrary angles of the pair with respect to its velocity. We compare our results with the case that no deformation parameter is in metric background. We will see that the thermal width of the pair increases with increasing deformation parameter. Also, for nonzero values of deformation parameter the pair feels moving plasma in all distances. In addition our results indicate that contribution of deformation parameter leads to larger dissociation length for the moving pair reverse to the effect of the pairs velocity in the plasma., Comment: 20 pages, 12 figures

In this paper, we study the holographic dark energy density and interacting extended Chaplygin gas energy density in the Einstein gravity. We reconstruct the scalar field and the scalar potential describing the extended Chaplygin gas. In the special case, we obtain energy density and investigate some cosmological parameters. Assuming interaction between components we find energy density for some different parametrization of total EoS. We analyze tensor to scalar ratio and use recent observational data of BICEP2 to fix the model parameters., Comment: 15 pages, 3 figures, References added in version 2

In this note we consider the logarithmic curvature correction to Lifshitz and hyper scaling violation geometries. We investigate the effect of this correction to the gauge kinetic function f and the effective potential V . For the case of hyper scaling violating we show that the coupling between dilaton and the correction terms exhibit the logarithmic behavior for dilaton like for the case of squared curvature correction. We find the unexpected form of gauge kinetic function and potential in the presence of logarithmic terms. We try to resolve the IR singularity of Lifshitz and hyperscaling violation geometries by adding the logarithmic term., Comment: 10 pages

In this paper, we investigate the dynamics of a heavy quark under the plasmas correspond to three dimensional hairy black holes. We utilize the AdS/CFT correspondence to study the holographic Brownian motion of this particle in different kinds of hairy black holes. For uncharged black hole at low frequency limit we derive analytic expressions for correlation functions and response functions and verify that the fluctuation-dissipation theorem holds in the presence of a scalar field in the metric background. In the case of charged black hole, we think that the results are similar to what derived for uncharged black hole., Comment: 15 pages

In this paper we construct rotating charged hairy black hole in (2+1) dimensions for infinitesimal black hole charge and rotation parameters. Then we consider this black hole as particle accelerator and calculate the center-of-mass energy of two colliding test particles near the rotating charged hairy black hole in (2+1) dimensions. As we expected, the center-of-mass energy has infinite value., Comment: 12 pages

In this paper we consider Tachyonic scalar field as dark energy with interaction between components in the case of variable $G$ and $\Lambda$. We assume a flat Universe with specific form of scale factor and study cosmological parameters numerically and graphically. Statefinder analysis also performed as well. In the special choice of interaction parameters we succeed to obtain analytical expression of densities. We find that our model will be stable in the late stage but there is an instability at the early Universe., Comment: 17 pages, accepted by Research in Astronomy and Astrophysics (RAA). arXiv admin note: text overlap with arXiv:1402.2592 by other authors

In the large 't Hooft coupling limit, the hadronic size of baryon is small and nucleon-nucleon potential is obtained from massless pseudo-scalar exchanges and an infinite tower of spin one mesons exchanges. In this paper we use the holographic nucleon-nucleon interaction and obtain the corresponding potential and binding energy for deuteron and tritium nuclei. The obtained potentials are repulsive at short distances and clearly become zero by increasing distance as we expected.

In this paper we study the behavior of jet quenching parameter in the background metric with hyperscaling violation at finite temperature.The background metric is covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent z and hyperscaling exponent $\theta$. We evaluate the jet quenching parameter for certain range of these parameters consistent with the Gubser bound conditions in terms of T, z and $\theta$. We compare our results with those from conformal case and experimental data. Then we add a constant electric field to this background and find its effect on the jet quenching parameter., Comment: 22 pages, 9 figures