Search

Recently a general prescription for determining the vacuum modular flow generator and the corresponding modular Hamiltonian in the BMS-invariant field theories (BMSFTs) have provided by Apolo et. al \cite{Apolo}. According to this paper Einstein gravity in asymptotically flat three-dimensional spacetimes is dual to a BMSFT. In the present paper we extend this study to the generalized minimal massive gravity model (GMMG). So we study some aspects of $Flat_3/BMSFT$ holography in the framework of this model. We derive the modular Hamiltonian for single intervals in thermal and non-thermal BMSFTs and show its holographic dual is the gravitational charge associated with isometries that preserve the asymptotic form of the metric. Also using the modular Hamiltonian we derive the first law of entanglement entropy. Our results for GMMG model reduces to the result for Einstein gravity in $2+1$ dimension, when $\mu , m^2 \to \infty $, and $\sigma=-1$. These limiting cases, are a place in parameter space of model, where GMMG model reduces to the Einstein gravity., Comment: 17 pages

We focus on a proper candidate for the entanglement wedge in asymptotically flat bulk geometries that are described by the generalized minimal massive gravity (GMMG) in the context of the flat holography. To this end, we describe the boundary by two dimensional Galilean conformal field theory (GCFT) at the bipartite mixed state of the two disjoint intervals. We make a conjecture on the minimal entanglement wedge cross section (EWCS) and we find that the results are consistent with the previous computations on the holographic entanglement negativity., Comment: 20 pages, 3 figures

In this work, we study the holographic entanglement entropy of two dimensional $T\bar{T}$-deformed conformal field theory. We compute the correction due to the deformation up to the leading order of the deformation parameter in the framework of New massive gravity, General minimal massive gravity, and Exotic general massive gravity. We also apply Song's prescription to obtain the entanglement entropy for deformed theories. In each cases, we find agreement between the results., Comment: 13 pages

We extend the reflected entropy to the bipartite state in a two dimensional Galilean conformal field theory ($GCFT_2$) which is dual to the asymptotically flat spacetime described by the generalized minimal massive gravity (GMMG). To this end we consider the Renyi entanglement entropy formula that can be related to the reflected entropy by some manipulations of the replica technique. In a limited case, we find the reflected entropy is twice the minimal entanglement wedge cross section (EWCS) and this is an evidence on the relation between the reflected entropy and the EWCS in the flat holography scenario., Comment: 26 pages, 5 figures

We study some aspects of a class of non-AdS holography where the 3d bulk gravity is given by Generalized Minimal Massive Gravity (GMMG). We consider the spacelike warped $AdS_3$ ($WAdS_3$) black hole solution of this model where the 2d dual boundary theory is the warped conformal field theory (WFCT). The charge algebra of the isometries in the bulk and the charge algebra of the vacuum symmetries at the boundary are compatible and this is an evidence for the duality conjecture. Further evidence for this duality is the equality of entanglement entropy and modular Hamiltonian on both sides of the duality. So we consider the modular Hamiltonian for the single interval at the boundary in associated to the modular flow generators of the vacuum. We calculate the gravitational charge in associated to the asymptotic Killing vectors that preserve the metric boundary conditions. Assuming the first law of the entanglement entropy to be true, we introduce the matching conditions between the variables in two side of the duality and we find equality of the modular Hamiltonian variations and the gravitational charge variations in two sides of the duality. According to the results of the present paper we can say with more sure that the dual theory of the warped $AdS3$ black hole solution of GMMG is a Warped CFT., Comment: 23 pages. Accepted for publication in EPJC

In this work, following the paper by Romain Ruzziconi and C\'eline Zwikel \cite{Ruzziconi:2020wrb} we extend the questions of conservation, integrability and renormalization in Bondi gauge and in GR to the theory of Topological Massive Gravity (TMG). We construct the phase space and renormalize the divergences arising within the symplectic structure through a holographic renormalization procedure. We show that the charge expressions are generically finite, conserved and can be made integrable by a field$-$dependent redefinition of the asymptotic symmetry parameters., Comment: 14 pages. arXiv admin note: text overlap with arXiv:2012.03961 by other authors

The vacuum expectation value of the current density for a charged scalar field is investigated in Rindler spacetime with a part of spatial dimensions compactified to a torus. It is assumed that the field is prepared in the Fulling-Rindler vacuum state. For general values of the phases in the periodicity conditions and the lengths of compact dimensions, the expressions are provided for the Hadamard function and vacuum currents. The current density along compact dimensions is a periodic function of the magnetic flux enclosed by those dimensions and vanishes on the Rindler horizon. The obtained results are compared with the corresponding currents in the Minkowski vacuum. The near-horizon and large-distance asymptotics are discussed for the vacuum currents around cylindrical black holes. In the near-horizon approximation the lengths of compact dimensions are determined by the horizon radius. At large distances from the horizon the geometry is approximated by a locally anti-de Sitter spacetime with toroidally compact dimensions and the lengths of compact dimensions are determined by negative cosmological constant., Comment: 16 pages, 2 figures, discussion and references added

We study the inflationary period driven by a fermionic field which is non-minimally coupled to gravity in the context of the constant-roll approach. We consider the model for a specific form of coupling and perform the corresponding inflationary analysis. By comparing the result with the Planck observations coming from CMB anisotropies, we find the observational constraints on the parameters space of the model and also the predictions the model. We find that the values of $r$ and $n_{s}$ for $-1.5<\beta\leq-0.9$ are in good agreement with the observations when $|\xi|=0.1$ and $N=60$., Comment: 7 pages, 2 figures

In this work, we investigate the near horizon and asymptotic symmetries of static and rotating hairy$-$AdS black hole in the framework of general minimal massive gravity. We obtain energy, angular momentum and entropy of the solutions. Then we show that our results for these quantities are consistent with the first law of black hole thermodynamics. By considering the near horizon geometry of black hole, we find near horizon conserved charges and their algebra. By writing the algebra of conserved charges in terms of Fourier modes we have obtained the conserved charges in terms of zero modes., Comment: 14 pages. V2: 18 pages, matches the published version

In this paper we study the application of holographic entanglement negativity proposal for bipartite states in the 2d Galilean conformal field theory ($GCFT_2$) dual to bulk asymptotically flat spacetimes in the context of generalized minimal massive gravity (GMMG) model. $GCFT_2$ is considered on the boundary side of the duality and the bulk gravity is described by GMMG that is asymptotically symmetric under the Galilean conformal transformations. In this paper, the replica technique, based on the two-point and the four-point twist correlators, is utilized and the entanglement entropy and the entanglement negativity are obtained in the bipartite configurations of the system in the boundary., Comment: 28 pages

Attempts to find black hole microstates using the Hamiltonian phase space approach have been made on the Schwarzschild spacetime. Since the Schwarzschild spacetime is also in the larger family of the Kerr spacetimes, and both are asymptotically flat, the Kerr black hole is a good option for the method development. The Kerr black hole is a spinning one. We perform this analysis on the Kerr spacetime and we obtain promising results using the covariant phase space analysis. Although we have forced ourselves to use the Bondi fall-off conditions, we find the gauge degrees of freedom that could be good candidates for the black hole microstates. The charge algebra on the boundary could be a Virasoro algebra that has a different central term than the Schwarzschild black hole. The two dimensional theory on the black hole boundary is conjectured to be conformally invariant., Comment: 25 pages, reference and paragraphs added

Recently, black hole symmetries have been studied widely and it has been speculated that this procedure will lead to the deeper understanding of the black hole physics. Spontaneous symmetry breaking of the horizon symmetries is one of the very recent attempt to clarify black hole thermal physics. In this work, we are going to investigate the same in three dimensional massive gravity, including higher order of Riemann tensor. We observe that the idea also works well in this gravitational theory, thereby providing stronger demand of the viability of this idea., Comment: 17 Pages

Previously we have studied the Generalized Minimal Massive Gravity (GMMG) in asymptotically $AdS_3$ background, and have shown that the theory is free of negative-energy bulk modes. Also we have shown GMMG avoids the aforementioned bulk-boundary unitarity clash. Here instead of $AdS_3$ space we consider asymptotically flat space, and study this model in the flat limit. The dual field theory of GMMG in the flat limit is a $BMS_3$ invariant field theory, dubbed (BMSFT) and we have BMS algebra asymptotically instead of Virasoro algebra. In fact here we present an evidence for this claim. Entanglement entropy of GMMG is calculated in the background in the flat null infinity. Our evidence for mentioned claim is the result for entanglement entropy in filed theory side and in the bulk (in the gravity side). At first using Cardy formula and Rindler transformation, we calculate entanglement entropy of BMSFT in three different cases. Zero temperature on the plane and on the cylinder, and non-zero temperature case. Then we obtain the entanglement entropy in the bulk. Our results in gravity side are exactly in agreement with field theory calculations., Comment: 17 pages, reference and paragraphs added

Flat Space Cosmology (FSC) spacetimes are exact solutions of 3D gravity theories. In this work, we study phase transition between FSC spacetimes and Hot Flat Spacetimes (HFS) in general minimal massive gravity and exotic general massive gravity. We show that similar to topological massive gravity the tunneling occurs between two spacetimes by comparing their free energies. We also obtain the corrections to the Bekenstein-Hawking entropy, and its effect on the phase transition is studied., Comment: 13 pages, typos corrected, main results and conclusion unchanged, reference and paragraph added

Recently it has been speculated that a set of diffeomorphisms exist which act non-trivially on the horizon of some black holes such as Kerr and Kerr-Newman black hole. %\cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant phase space formalism one can obtain conserved charges as surface integrals on the horizon. Kerr-Bolt spacetime is well-known for its asymptotic topology and has been studied widely in recent years. In this work we are going to study Kerr-Bolt black hole and provide a holographic description of it in term of warped conformal field theory., Comment: 12 pages

Recently it has been speculated that a set of infinitesimal ${\rm Virasoro_{\,L}}\otimes{\rm Virasoro_{\,R}}$ diffeomorphisms exist which act non-trivially on the horizon of some black holes such as kerr and Kerr-Newman black hole \cite{Haco:2018ske,Haco:2019ggi}. Using this symmetry in covariant phase space formalism one can obtains Virasoro charges as surface integrals on the horizon. Kerr-Bolt spacetime is well-known for its asymptotically topology and has been studied widely in recent years. In this work we are interested to find conserved charge associated to the Virosora symmetry of Kerr-Bolt geometry using covariant phase space formalism. We will show right and left central charge are $c_R=c_L=12 J$ respectively. Our results also show good agreement with Kerr spacetime in the limiting behavior., Comment: 11 pages

In the first part of the present work, the correction to photon emission rate of an oscillating two-level atom in the presence of electromagnetic quantum vacuum field has been investigated for two different configurations: (i) Atom is trapped in the vicinity of a perfect conductor (ii) Atom is trapped between two perfect conductors. In the second part, the correction to the decay rate of an initially excited oscillating two-level atom due to the presence of a perfect conducting surface is found., Comment: 18 pages, 6 figures

In this paper, the linearized field equations related to the quadratic curvature gravity theory have been obtained in the four-dimensional de Sitter (dS) space-time. The massless spin-2 field equations have been written in terms of the Casimir operators of dS group making use of the ambient space notations. By imposing some simple constraints, arisen from group theoretical interpretation of the field equations, a new four-dimensional Gauss-Bonnet (GB)-like action has been introduced with the related field equations transforming according to the unitary irreducible representations (UIR's) of dS group. Since, the field equations transform according to the UIR's of dS group, the GB-like action, we just obtained, is expected to be a successful model of modified gravity. For more clarifying, the gauge invariant field equations have been solved in terms of a gauge-fixing parameter ${\cal{C}}$. It has been shown that the solution can be written as the multiplication of a symmetric rank-2 polarization tensor and a massless minimally coupled scalar field on dS space. The Gupta-Bleuler quantization method has been utilized and the covariant two-point function has been calculated in terms of the massless minimally coupled scalar two-point function, using the ambient space notations. It has been written in terms of dS intrinsic coordinates from the ambient space counterpart. The two-point functions are dS invariant and free of any theoretical problems. It means that the proposed model is a successful model of modified gravity and it can produce significant results in the contexts of classical theory of gravity and quantum gravity toy models., Comment: 17 pages. arXiv admin note: text overlap with arXiv:1601.03946

In this article, the new black hole solutions to the Einstein-power-Maxwell-dilaton gravity theory have been investigated in a four-dimensional space-time. The coupled scalar, electromagnetic and gravitational field equations have been solved in a static and spherically symmetric geometry. It has been shown that dilatonic potential, as the solution to the scalar field equation, can be written in the form of a generalized Liouville potential. Also, three classes of novel charged dilaton black hole solutions, in the presence of power law nonlinear electrodynamics, have been constructed out which are asymptotically non-flat and non-AdS. The conserved and thermodynamic quantities have been calculated from geometrical and thermodynamical approaches, separately. Since the results of these two alternative approaches are identical one can argue that the first law of black hole thermodynamics is valid for all of the new black hole solutions. The thermodynamic stability or phase transition of the black holes have been studied, making use of the canonical ensemble method. The points of type-1 and type-2 phase transitions as well as the ranges at which the black holes are stable have been indicated by considering the heat capacity of the new black hole solutions. The global stability of the black holes have been studied through the grand canonical ensemble method. Regarding the Gibbs free energy of the black holes, the points of Hawking-Page phase transition and ranges of the horizon radii at which the black holes are globally stable have been determined., Comment: 21 pages with 9 captioned figures

Starting from an engineered periodic optical structure formed by waveguide arrays comprised of two interleaved lattices, we simulate a deformed Dirac equation. We show that the system also simulate graphene nano ribbons under strain. This optical analogue allows us to study the phenomenon of Zitterbewegung for the modified Dirac equation. Our results show that the amplitude of Zitterbewegung oscillations changes as the deformation parameter is changed.

In this paper, we study the problem of massless particle creation in a flat, homogeneous and isotropic universe in the framework of $f(G)$ gravity. The Bogolyubov coefficients are calculated for the accelerating power-law solutions of the model in a matter dominated universe, from which the total number of created particle per unit volume of space can be obtained. It is proved that the total particle density always has a finite value. Therefore, the Bogolyubov transformations are well-defined and the Hilbert spaces spanned by the vacuum states at different times are unitarily equivalent. We find that the particles with small values of the mode $k$ are produced in the past and particles with large values of $k$ are produced only in the future. The negative pressure resulting from the gravitational particle creation is also determined. It is then argued that this pressure even in the presence of energy density and thermal pressure may affect significantly the cosmic expansion., Comment: 10 pages, 4 figures, to be published in Astrophysics and Space Science. arXiv admin note: text overlap with arXiv:0911.0622, arXiv:1402.5004 by other authors

Einstein-Maxwell theory is not only covariant under diffeomorphisms but also is under $U(1)$ gauge transformations. We introduce a combined transformation constructed out of diffeomorphism and $U(1)$ gauge transformation. We show that symplectic potential, which is defined in covariant phase space method, is not invariant under combined transformations. In order to deal with that problem, following Donnelly and Freidel proposal \cite{1}, we introduce new fields. In this way, phase space and consequently symplectic potential will be extended. We show that new fields produce edge modes. We consider surface-preserving symmetries and we show that the group of surface-preserving symmetries is semi-direct sum of 2-dimensional diffeomorphism group on a spacelike codimension two surface with $SL(2,\mathbb{R})$ and $U(1)$. Eventually, we deduce that the Casimir of $SL(2,\mathbb{R})$ is the area element, similar to the pure gravity case \cite{1}., Comment: 18 pages

We calculate the transmission coefficient for a particle crossing a potential barrier in monolayer graphene with Rashba spin-orbit coupling and in bilayer graphene. We show that in both the cases one can go from Klein tunneling regime, characterized by perfect normal transmission, to anti-Klein tunneling regime, with perfect normal reflection, by tuning the Rashba spin-orbit coupling for a monolayer or the interplane coupling for a bilayer graphene. We show that the intermediate regime is characterized by a non-monotonic behavior with oscillations and resonances in the normal transmission amplitude as a function of the coupling and of the potential parameters., Comment: 9 pages, 5 figures

We consider near horizon fall-off conditions of stationary black holes in Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry generator that preserves near horizon fall-off conditions. Subsequently, we find supertranslation, superrotation and multiple-charge modes. We apply the obtained results on a typical static dilaton black hole and on a charged rotating black string, as examples. In this case, supertranslation double-zero-mode charge $\mathcal{T}_{(0,0)}$ is not equal to black hole entropy times Hawking temperature. This may be seen as a problem but it is not, because, in Einstein-Maxwell-Dilaton theory, we have a U(1) gauge freedom and we use an appropriate gauge fixing to fix that problem. We show that new entropy formula $4 \pi \hat{J}^{+}_{0} \hat{J}^{-}_{0}$, proposed in \cite{17}, is valid for black strings as well as black holes., Comment: 15 pages. arXiv admin note: substantial text overlap with arXiv:1802.04665

In this paper, we examine the validity of the first law of inner mechanics of black holes in Generalized Minimal Massive Gravity. We consider BTZ and spacelike warped black holes and show that the first law of inner mechanics is valid for given black holes in Generalized Minimal Massive Gravity. As we expect, due to the presence of the Lorentz Chern-Simons term in Lagrangian of considered model, the product of the entropies of the inner and outer horizons depends on the mass as it happens in Topologically Massive Gravity.

In this paper we provide the first non-trivial evidence for universality of the entropy formula $4\pi J_{0}^{+}J_{0}^{-}$ beyond pure Einstein gravity in 4-dimensions. We consider the Einstein-Maxwell theory in the presence of cosmological constant, then write near horizon metric of the Kerr-Newman (A)dS black hole in the Gaussian null coordinate system. We consider near horizon fall-off conditions for metric and $U(1)$ gauge field. We find asymptotic combined symmetry generator, consists of diffeomorphism and $U(1)$ gauge transformation, so that it preserves fall-off conditions. Consequently, we find supertranslation, supperrotation and multiple-charge modes and then we show that the entropy formula is held for the Kerr-Newman (A)dS black hole. Supperrotation modes suffer from a problem. By introducing new combined symmetry generator, we cure that problem., Comment: 16 pages. Version published in JHEP

We consider spacelike warped AdS$_{3}$ black hole metric in Boyer-Lindquist coordinate system. We present a coordinates transformation so that it maps metric in Boyer-Lindquist coordinates to the one in Gaussian null coordinates. Then we introduce new fall-off conditions near the horizon of non-extremal warped black holes. We study the near horizon symmetry algebra of such solutions in the context of Generalized minimal massive gravity. Similar to the black flower solutions, also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the warped black flower solutions. We show that the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the warped black hole., Comment: 15 pages, no figure. arXiv admin note: text overlap with arXiv:1701.00209, arXiv:1606.05260. NOTE ADDED

This paper deals with the problem of defining off-shell conserved charges in a set of theories known as Chern-Simons-like theories of gravity (CSLTG). The method is derived in a general way, which may find applications in a wide set of theories, and then specified to the case of Generalized minimal massive gravity (GMMG), where known results of the central charge and black hole entropy are reproduced. The results for the charges are useful to the community and can be applied to all three-dimensional gravity theories within the class of CSLTG which includes almost all of them. The given specific examples show a consistency check of the more general method.

In this paper we present the generalization of Chern-Simons-like theories of gravity (CSLTG) to spin-3. We propose a Lagrangian describing the spin-3 fields coupled to Chern-Simons-like theories of gravity. Then we obtain conserved charges of these theories by using a quasi-local formalism. We find a general formula for entropy of black holes solutions of Spin-3 CSLTG. As an example, we apply our formalism to the spin-3 Generalized minimal massive gravity (GMMG) model. We analysis this model at linearized level and show that this model propagate two massive spin-2 modes and two massive spin-3 modes. We find no-ghost and no-tachyon conditions, which can be satisfy in the parameter space of the model. Then we find energy, angular momentum and entropy of a special black hole solution of this model., Comment: 29 pages

We apply the new fall of conditions presented in the paper \cite{10} on asymptotically flat spacetime solutions of Chern-Simons-like theories of gravity. We show that the considered fall of conditions asymptotically solve equations of motion of generalized minimal massive gravity. We demonstrate that there exist two type of solutions, one of those is trivial and the others are non-trivial. By looking at non-trivial solutions, for asymptotically flat spacetimes in the generalized minimal massive gravity, in contrast to Einstein gravity, cosmological parameter can be non-zero. We obtain the conserved charges of the asymptotically flat spacetimes in generalized minimal massive gravity, and by introducing Fourier modes we show that the asymptotic symmetry algebra is a semidirect product of a $BMS_{3}$ algebra and two $U(1)$ current algebras. Also we verify that the $BMS_{3}$ algebra can be obtained by a contraction of the AdS$_3$ asymptotic symmetry algebra when the AdS$_3$ radius tends to infinity in the flat-space limit. Finally we find energy, angular momentum and entropy for a particular case and deduce that these quantities satisfy the first law of flat space cosmologies., Comment: 16 pages. arXiv admin note: text overlap with arXiv:1701.00209

This article is devoted to static spherically symmetric black hole solutions of dRGT (de Rham-Gabadadze-Tolley) massive gravity in the presence of cosmological constant. The unitary and non-unitary gauges are used to find the solutions in three, four and five dimensions. We show that there are two general classes of solutions. In one of them, the effect of massive potential is appeared as the effective cosmological constant. By investigating these solutions in different dimensions, we find an expression for effective cosmological constant in arbitrary dimensions., Comment: Version accepted for publication in PLB

We evaluate the Hadamard function, the vacuum expectation values (VEVs) of the field squared and the energy-momentum tensor for a massive scalar field with general curvature coupling parameter in the geometry of two parallel plates on a spatially flat Friedmann-Robertson-Walker background with a general scale factor. On the plates, the field operator obeys the Robin boundary conditions with the coefficients depending on the scale factor. In all the spatial regions, the VEVs are decomposed into the boundary-free and boundary-induced contributions. Unlike to the problem with the Minkowski bulk, in the region between the plates the normal stress is not homogeneous and does not vanish in the geometry of a single plate. Near the plates, it has different signs for accelerated and deccelerated expansions of the universe. The VEV of the energy-momentum tensor, in addition to the diagonal components, has a nonzero off-diagonal component describing an energy flux along the direction normal to the boundaries. Expressions are derived for the Casimir forces acting on the plates. Depending on the Robin coefficients and on the vacuum state, these forces can be either attractive or repulsive. An important difference from the corresponding result in the Minkowski bulk is that the forces on the separate plates, in general, are different if the corresponding Robin coefficients differ. We give the applications of general results for the class of $\alpha $-vacua in the de Sitter bulk. It is shown that, compared with the Bunch-Davies vacuum state, the Casimir forces for a given $\alpha $-vacuum may change the sign., Comment: 20 pages, no figure. Version accepted for publication in PRD

In this paper we show that warped AdS$_{3}$ black hole spacetime is a solution of the generalized minimal massive gravity (GMMG) and introduce suitable boundary conditions for asymptotically warped AdS$_{3}$ spacetimes. Then we find the Killing vector fields such that transformations generated by them preserve the considered boundary conditions. We calculate the conserved charges which correspond to the obtained Killing vector fields and show that the algebra of the asymptotic conserved charges is given as the semi direct product of the Virasoro algebra with $U(1)$ current algebra. We use a particular Sugawara construction to reconstruct the conformal algebra. Thus, we are allowed to use the Cardy formula to calculate the entropy of the warped black hole. We demonstrate that the gravitational entropy of the warped black hole exactly coincide with what we obtain via Cardy's formula. As we expect the warped Cardy formula also give us exactly the same result which we obtain from usual Cardy's formula. We calculate mass and angular momentum of the warped black and then check that obtained mass, angular momentum and entropy satisfy first law of the black hole mechanics. According to the results of this paper we belief that the dual theory of the warped AdS$_{3}$ black hole solution of GMMG is a Warped CFT., Comment: 24 pages, accepted for publication in Class. Quant. Grav. (2017)

We study the dynamics of interacting holographic dark energy model in Brans-Dicke cosmology for the future event horizon and the Hubble horizon cut-offs. We determine the system of first-order differential equations for the future event horizon and Hubble horizon cut-offs, and obtain the corresponding fixed points, attractors, repellers and saddle points. Finally, we investigate the cosmic coincidence problem in this model for the future event horizon and Hubble horizon cut-offs and find that for both cut-offs and for a variety of Brans-Dicke parameters the coincidence problem is almost resolved., Comment: 14 pages, two figures, revised

We consider a metric which describes Ba$\tilde{\text{n}}$ados geometries and show that the considered metric is a solution of generalized minimal massive gravity (GMMG) model. We consider the Killing vector field which preserves the form of considered metric. Using the off-shell quasi-local approach we obtain the asymptotic conserved charges of given solution. Similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also, we show that the algebra among the asymptotic conserved charges is isomorphic to two copies of the Virasoro algebra. Eventually, we find relation between the algebra of the near horizon and the asymptotic conserved charges. This relation show that the main part of the horizon fluffs proposal of Refs.\cite{140,14} appear for generic black holes in the class of Ba$\tilde{\text{n}}$ados geometries in the context of GMMG model., Comment: 12 pages. arXiv admin note: text overlap with arXiv:1606.05260

We study the inflation via logarithmic entropy-corrected holographic dark energy LECHDE model with future event horizon, particle horizon and Hubble horizon cut-offs, and compare the results with those of obtained in the study of inflation by holographic dark energy HDE model. In comparison, the spectrum of primordial scalar power spectrum in the LECHDE model becomes redder than the spectrum in HDE model. Moreover, the consistency with the observational data in LECHDE model of inflation, constrains the reheating temperature and Hubble parameter by one parameter of holographic dark energy and two new parameters of logarithmic corrections., Comment: 11 pages, 10 figures

In this paper we consider the Einstein-Maxwell theory and define a combined transformation composed of diffeomorphism and $U(1)$ gauge transformation. For generality, we assume that the generator $\chi$ of such transformation is field-dependent. We define the extended off-shell ADT current and then off-shell ADT charge such that they are conserved off-shell for the asymptotically field-dependent symmetry generator $\chi$. Then, we define the conserved charge corresponding to the asymptotically field-dependent symmetry generator $\chi$. We apply the presented method to find the conserved charges of the asymptotically AdS$_{3}$ spacetimes in the context of the Einstein-Maxwell theory in three dimensions. Although the usual proposal for the quasi local charges provides divergent global charges for the Einstein-Maxwell theory with negative cosmological constant in three dimensions, here we avoid this problem by introducing proposed combined transformation $\chi$., Comment: 17 pages

We study the structure formation by investigating the spherical collapse model in the context of new agegraphic dark energy model in flat FRW cosmology. We compute the perturbational quantities $g(a)$, $\delta_{c}(z_{c})$, $\lambda(z_{c})$, $\xi(z_{c})$, $\Delta_{vir}(z_{c})$, $\log[\nu f(\nu)]$ and $\log[n(k)]$ for the new agegraphic dark energy model and compare the results with those of EdS and $\Lambda CDM$ models. We find that there is a dark energy dominated universe at low redshifts and a matter dominated universe at high redshifts in agreement with observations. Also, the size of structures, the overdense spherical region, and the halo size in the new agegraphic dark energy model are found smaller, denser, and larger than those of EdS and $\Lambda CDM$ models. We compare our results with the results of tachyon scalar field and holographic dark energy models., Comment: 9 pages, 15 figures

In this paper we consider a generally covariant theory of gravity, and extend the generalized off-shell ADT current such that it becomes conserved for field dependent (asymptotically) Killing vector field. Then we define the extended off-shell ADT current and the extended off-shell ADT charge. Consequently, we define the conserved charge perturbation by integrating from the extended off-shell ADT charge over a spacelike codimension two surface. Eventually, we use the presented formalism to find the conserved charge perturbation of an asymptotically flat spacetime. The conserved charge perturbation we obtain is exactly matched with the result of the paper \cite{6'}. These charges are as representations of the $BMS_4$ symmetry algebra. Also, we find that the near horizon conserved charges of a non-extremal black hole with extended symmetries are the Noether charges. For this case our result is also exactly matched with that of the paper \cite{15}., Comment: 16 pages

We study the tachyon scalar field model in flat FRW cosmology with the particular potential $\phi^{-2}$ and the scale factor behavior $a(t)=t^n$. We consider the spherical collapse model and investigate the effects of the tachyon scalar field on the structure formation in flat FRW universe. We calculate $\delta_{c}(z_{c})$, $\lambda(z_{c})$, $\xi(z_{c})$, $\Delta_{V}(z_{c})$, $\log [\nu f(\nu)]$ and $\log [n(k)]$ for the tachyon scalar field model and compare the results with the results of EdS model and $\Lambda CDM$ model. It is shown that in the tachyon scalar field model the structure formation may occur earlier, in comparison to the other models., Comment: 14 pages, 15 figures, revision

In this paper we study the near horizon symmetry algebra of the non-extremal black hole solutions of the Chern-Simons-like theories of gravity, which are stationary but are not necessarily spherically symmetric. We define the extended off-shell ADT current which is an extension of the generalized ADT current. We use the extended off-shell ADT current to define quasi-local conserved charges such that they are conserved for Killing vectors and asymptotically Killing vectors which depend on dynamical fields of the considered theory. We apply this formalism to the Generalized Minimal Massive Gravity( GMMG) and obtain conserved charges of a spacetime which describes near horizon geometry of non-extremal black holes. Eventually, we find the algebra of conserved charges in Fourier modes. It is interesting that, similar to the Einstein gravity in the presence of negative cosmological constant, for the GMMG model also we obtain the Heisenberg algebra as the near horizon symmetry algebra of the black flower solutions. Also the vacuum state and all descendants of the vacuum have the same energy. Thus these zero energy excitations on the horizon appear as soft hairs on the black hole., Comment: 19 pages, added discussion and references

Restricting the covariant gravitational phase spaces to the manifold of parametrized families of solutions, the mass, angular momenta, entropies, and electric charges can be calculated by a single and simple method. In this method, which has been called "solution phase space method," conserved charges are unambiguous and regular. Moreover, assuming the generators of the charges to be exact symmetries, entropies and other conserved charges can be calculated on almost arbitrary surfaces, not necessarily horizons or asymptotics. Hence, the first law of thermodynamics would be a local identity relating the exact symmetries to which the mass, angular momentum, electric charge, and entropy are attributed. In this paper, we apply this powerful method to the $f(R)$ gravitational theories accompanied by the terms quadratic in the Riemann and Ricci tensors. Furthermore, conserved charges and the first law of thermodynamics for some of their black hole solutions are exemplified. The examples include warped AdS$_3$, charged static BTZ, and 3-dimensional $z=3$ Lifshitz black holes., Comment: 21 pages, synchronized with the published version

We consider the Generalized Minimal Massive Gravity (GMMG) model in the first order formalism. We show that all the solutions of the Einstein gravity with negative cosmological constants solve the equations of motion of considered model. Then we find an expression for the off-shell conserved charges of this model. By considering the near horizon geometry of a three dimensional black hole in the Gaussian null coordinates, we find near horizon conserved charges and their algebra. The obtained algebra is centrally extended. By writing the algebra of conserved charges in terms of Fourier modes and considering the BTZ black hole solution as an example, one can see that the charge associated with rotations along $\mathcal{Y}_{0}$ coincides exactly with the angular momentum, and he charge associated with time translations $\mathcal{T}_{0}$ is the product of the black hole entropy and its temperature. As we expect, in the limit when the GMMG tends to the Einstein gravity, all the result we obtain in this paper reduce to the result of the paper \cite{5}., Comment: 14 pages

Recently, the theory of Topologically massive gravity non-minimally coupled to a scalar field has been proposed which comes from Lorentz-Chern-Simons theory \cite{1}. That theory is a torsion free one. We extend that theory by adding an extra term which makes torsion to be non-zero. The extended theory can be regarded as an extension of Minimal massive gravity such that it is non-minimally coupled to a scalar field. We obtain equations of motion of extended theory such that they are expressed in terms of usual torsion free spin-connection. We show that BTZ spacetime is a solution of this theory when scalar field is constant. We define quasi-local conserved charge by the concept of generalized off-shell ADT current which both are conserved for any asymptotically Killing vector field as well as a Killing vector field which is admitted by spacetime everywhere. Also we find general formula for entropy of stationary black hole solution in the context of considered theory. We apply the obtained formulas on BTZ black hole solution, to calculate energy, angular momentum and entropy of this soultion. We obtain the central extension term, the central charges and the eigenvalues of the Virasoro algebra generators for the BTZ black hole solution. We calculate energy and angular momentum of BTZ black hole using the eigenvalues of the Virasoro algebra generators. Also we calculate the entropy of BTZ black hole by using the Cardy formula. We find that obtained results using two different ways are exactly matched as we expected., Comment: 22 pages, no figure

We investigate the cosmological dynamics of interacting Logarithmic Entropy Corrected Holographic Dark Energy model with Cold Dark Matter. Fixed points are determined and their corresponding cosmological models are presented. Moreover, the dynamical properties of these fixed points are derived., Comment: 8 pages, Published online, Int. J. Mod. Phys. D (2016)

In this paper, we consider spin-3 Chern-Simons-like theories of gravity as extended theories of spin-3 gravity in (2+1)- dimension. In order to determine the number of local degrees of freedom we present the Hamiltonian formulation of these theories. We extract the Hamiltonian density, then we find primary and secondary constraints of these theories. Then we obtain the Poisson brackets of the primary and the secondary constraints. After that we count the number of local degrees of freedom of spin-3 Chern-Simons-like theories of gravity. We apply this method on spin-3 Einstein-Cartan gravity and spin-3 topologically massive gravity. According to the our results the spin-3 Einstein-Cartan gravity and the spin-3 topologically massive gravity have respectively zero and one bulk local degree of freedom., Comment: 10 pages, no figure

In this paper we obtain conserved charges of spin-3 topologically massive gravity by using a quasi-local formalism. We find a general formula to calculate conserved charge of the spin-3 topologically massive gravity which corresponds to a Killing vector field $\xi$. We show that this general formula reduces to the previous one for the ordinary spin-3 gravity presented in \cite{31} when we take into account only transformation under diffeomorphism, without considering generalized Lorentz gauge transformation (i.e. $\lambda _{\xi} =0$), and by taking $\frac{1}{\mu}\rightarrow 0$. Then we obtain a general formula for the entropy of black hole solutions of the spin-3 topologically massive gravity. Finally we apply our formalism to calculate energy, angular momentum and entropy of a special black hole solution and we find that obtained results are consistent with previous results in the limiting cases. Moreover our result for energy, angular momentum and entropy are consistent with the first law of black hole mechanics., Comment: 24 pages

The Chern-Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome to these problems by considering the concept of total variation and the Lorentz-Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches with the one obtained by the concept of the off-shell conserved charges., Comment: 19 pages. In Press by Nucl. Phys. B (2016). doi:10.1016/j.nuclphysb.2016.05.020