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A. Rezaei-Aghdam

Publications and source records attributed to A. Rezaei-Aghdam.

At least 19 recordsLinked to original sources
arXiv2025

Integrable sigma models with complex and generalized complex structures

Using the general method presented by Mohammedi \cite{NM} for the integrability of a sigma model on a manifold, we investigate the conditions for having an integrable deformation of the general sigma model on a manifold with a complex structure. On a Lie group, these conditions are satisfied by using the zeros of the Nijenhuis tensor. We then extend this formalism to a manifold, especially a Lie group, with a generalized complex structure. We demonstrate that, for the examples of integrable sigma models with generalized complex structures on the Lie groups $\mathbf{A_{4,8}}$ and $\mathbf{A_{4,10}}$, under special conditions, the perturbed terms of the actions are identical to the WZ terms.

hep-th↗
arXiv2024

Quasinormal modes of three $(2+1)$-dimensional black holes in string theory, conformal gravity, and Hu-Sawicki $F(R)$ theory via the Heun function

We study the propagation of massless fermionic fields, implementing a family of special functions: Heun functions, in solving the wave equation in three three-dimensional backgrounds, including the BTZ black hole in string theory and Lifshitz black hole solutions in conformal gravity and Hu-Sawicki $F(R)$ theory. The main properties of the selected black hole solutions is that their line elements are Weyl related to that of a homogeneous spacetime, whose spatial part possesses Lie symmetry, described by Lobachevsky-type geometry with arbitrary negative Gaussian curvature. Using the Weyl symmetry of massless Dirac action, we consider the perturbation equations of fermionic fields in relation to those of the homogeneous background, which having definite singularities, are transformed into Heun equation. We point out the existence of quasinormal modes labeled by the accessory parameter of the Heun function. The distribution of the quasinormal modes has been clarified to satisfy the boundary conditions that require ingoing and decaying waves at the event horizon and conformal infinity, respectively. It turned out that the procedure based on the Heun function, beside reproducing the previously known results obtained via hypergemetric function for the BTZ and Lifshitz black hole solution in conformal gravity, brings up new families of quasinormal frequencies, which can also contain purely imaginary modes. Also, the analysis of the quasinormal modes shows that with the negative imaginary part of complex frequencies $ω=ω_{Re}+iω_{Im}$, the fermionic perturbations are stable in this background.

hep-th↗
arXiv2024

Integrable sigma model with generalized $\mathcal{F}$ structure, Yang-Baxter sigma model with generalized complex structure and multi-Yang-Baxter sigma model

We construct an integrable sigma model with a generalized $\mathcal{F}$ structure, which involves a generalized Nijenhuis structure $\mathcal{J}$ satisfying $\mathcal{J}^{3}=-\mathcal{J}$. Utilizing the expression of the generalized complex structure on the metric Lie group manifold $G$ in terms of operator relations on its Lie algebra $\mathfrak{g}$, we formulate a Yang-Baxter sigma model with a generalized complex structure. Additionally, we present multi-Yang-Baxter sigma models featuring two and three compatible Nijenhuis structures. Examples for each of these models are provided.

hep-th↗
arXiv2023

Regular $(2+1)$-dimensional spatially homogeneous $α'$-corrected BTZ-like black hole in string theory

We consider a $(2+1)$-dimensional spacetime whose two-dimensional space part is Weyl-related to a surface of arbitrary negative constant Gaussian curvature with symmetries of two-dimensional Lie algebra. It is shown that the geometry is a Lobachevsky-type geometry described by deformed hyperbolic function. At leading order string effective action with the source given by dilaton and antisymmetric $B$-field in the presence of central charge deficit term $Λ$, we obtained a solution whose line element is Weyl-related to this homogeneous spacetime with arbitrary negative Gaussian curvature. The solution can be transformed to the BTZ-like black hole by coordinate redefinition, while the BTZ black hole can be recovered by choosing a special set of parameters. The solutions appear to be in the high curvature limit $Rα'\gtrsim1$, with emphasis on including the higher order $α'$ corrections. Considering the two-loop (first order $α'$) $β$-function equations of $σ$-model, we also present the $α'$-corrected black hole solutions.

hep-th↗
arXiv2022

(2+1)-dimensional f(R) gravity solutions via Hojman symmetry

In this paper, we use the Hojman symmetry approach to find new $(2+1)$-dimensional $f(R)$ gravity solutions, in comparison to Noether symmetry approach. In the special case of Hojman symmetry vector $X=R$, we recover $(2+1)$-dimensional BTZ black hole and generalized $(2+1)$-dimensional BTZ black hole solutions, obtained by Noether symmetry approach, and the interesting point is that the cosmological constant is appeared as the direct manifestation of Hojman symmetry.

gr-qc↗
arXiv2021

Leibniz bialgebras, classical Yang-Baxter equations and dynamical systems

This work is intended as an attempt to extend the notion of bialgebra for Lie algebras to Leibniz algebras and also, the correspondence between the Leibniz bialgebras and its dual is investigated. Moreover, the coboundary Leibniz bialgebras, the classical $r$-matrices and Yang-Baxter equations related to the Leibniz algebras are defined, and some examples are given. Finally, a method for construction of a dynamical system on a Leibniz manifold via Leibniz bialgebra is presented.

math-ph↗
arXiv2021

Spatially homogeneous black hole solutions in $z=4$ Hořava-Lifshitz gravity in $(4+1)$ dimensions with Nil geometry and $H^2\times R$ horizons

In this paper, we present two new families of spatially homogeneous black hole solution for $z=4$ Hořava-Lifshitz Gravity equations in $(4+1)$ dimensions with general coupling constant $λ$ and the especial case $λ=1$, considering $β=-1/3$. The three-dimensional horizons are considered to have Bianchi types $II$ and $III$ symmetries, and hence the horizons are modeled on two types of Thurston $3$-geometries, namely the Nil geometry and $H^2\times R$. Being foliated by compact 3-manifolds, the horizons are neither spherical, hyperbolic, nor toroidal, and therefore are not of the previously studied topological black hole solutions in Hořava-Lifshitz gravity. Using the Hamiltonian formalism, we establish the conventional thermodynamics of the solutions defining the mass and entropy of the black hole solutions for several classes of solutions. It turned out that for both horizon geometries the area term in the entropy receives two non-logarithmic negative corrections proportional to Hořava-Lifshitz parameters. Also, we show that choosing some proper set of parameters the solutions can exhibit locally stable or unstable behavior.

hep-th↗
arXiv2021

Classical and quantum (2+1)-dimensional spatially homogeneous string cosmology

We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $(2+1)$-dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge $B$-field, and central charge deficit term $Λ$. At the quantum level, solutions of Wheeler-DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm's mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level.

gr-qc↗
arXiv2020

FRW string cosmological solutions via Hojman symmetry

In this paper, we find exact string cosmological solutions for FRW cosmology, by using Hojman symmetry approach. The string cosmology under consideration includes a scalar field $ψ(t)$ with the potential $W(ψ)$, and a totally antisymmetric field strength $H_{μνρ}$ which is specifically defined in terms of the scale factor $a(t)$. We show that for this string cosmology, Hojman conserved quantities exist using which new exact solutions for the scale factor and the scalar field are obtained for specific potentials $W(ψ)$ with some free parameters. The presence of these parameters, together with those of arising from Hojman symmetry, is an important advantage using which one can construct the solutions $a(t)$ and $ψ(t)$ with variety of cosmological behaviors.

gr-qc↗
arXiv2019

New five-dimensional Bianchi type magnetically charged hairy topological black hole solutions in string theory

We construct black hole solutions to the leading order of string effective action in five dimensions with the source given by dilaton and magnetically charged antisymmetric gauge $B$-field. Presence of the considered $B$-field leads to the unusual asymptotic behavior of solutions which are neither asymptotically flat nor asymptotically (A)dS. We consider the three-dimensional space part to correspond to the Bianchi classes and so the horizons of these topological black hole solutions are modeled by seven homogeneous Thurston geometries of $E^3$, $S^3$, $H^3$, $H^2 \times E^1$, $\widetilde{SL_2R}$, nilgeometry, and solvegeometry. Calculating the quasi-local mass, temperature, entropy, dilaton charge, and magnetic potential, we show that the first law of black hole thermodynamics is satisfied by these quantities and the dilaton hair is of the secondary type. Furthermore, for Bianchi type $V$, the $T$-dual black hole solution is obtained which carries no charge associated with $B$-field and possesses a dilaton hair of secondary kind. Also, the entropy turns to be invariant under the $T$-duality.

hep-th↗
arXiv2019

Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries

We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find some examples of Jacobi-Lie Hamiltonian systems on real two- and three- dimensional Jacobi-Lie groups. Finally, we present Lie symmetries of Jacobi-Lie Hamiltonian systems on some three-dimensional real Jacobi-Lie groups.

math-ph↗
arXiv2019

Exchanging role of the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebras of bi-symplectic types

We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde {G}}}$ play the role of the symmetry groups of the systems. We give the new transformations to exchange the role of phase spaces and symmetry groups and obtain the relations between integrals of motions of these integrable systems. Finally, we give some examples of real four-dimensional Lie bialgebras of bi-symplectic type.

math-ph↗
arXiv2018

(2+1)-dimensional Chern-Simons bi-gravity with AdS Lie bialgebra as an interacting theory of two massless spin-2 fields

We introduce a new Lie bialgebra structure for the anti de Sitter (AdS) Lie algebra in (2+1)-dimensional spacetime. By gauging the resulting \textit{AdS Lie bialgebra}, we write a Chern-Simons gauge theory of bi-gravity involving two dreibeins rather than two metrics, which describes two interacting massless spin-2 fields. Our ghost-free bi-gravity model which has no any local degrees of freedom, has also a suitable free field limit. By solving its equations of motion, we obtain a \textit{new black hole} solution which has two curvature singularities and two horizons. We also study cosmological implications of this massless bi-gravity model.

hep-th↗
arXiv2018

Non-critical anisotropic Bianchi type $I$ string cosmology with $α'$-corrections

We present non-critical Bianchi type $I$ string cosmology solutions in the presence of central charge deficit term $Λ$. The leading order string frame curvature appears to be in the high curvature limit $Rα'\gtrsim1$, which underlines the necessity of including higher order $α'$-corrections. We give new solutions of two-loop (order $α'$) $β$-function equations of $σ$-model with non-zero $Λ$ and dilaton field in both cases of absence and presence of spatially homogeneous $H$-field ($H=dB$). Also, the evolution of solutions is studied in the Einstein frame, where the string effective action can transform to Gauss-Bonnet gravity model coupled to the dilaton field with potential. We study explicit examples in order $α'$ with chosen values of appeared constants in the solutions and discuss the cosmological implications.

hep-th↗
arXiv2018

(2+1)-dimensional interacting model of two massless spin-2 fields as a bi-gravity model

We propose a new group-theoretical (Chern-Simons) formulation for the bi-metric theory of gravity in (2+1)-dimensional spacetime which describe two interacting massless spin-2 fields. Our model has been formulated in terms of two dreibeins rather than two metrics. We obtain our Chern-Simons gravity model by gauging {\it mixed AdS-AdS Lie algebra} and show that it has a two dimensional conformal field theory (CFT) at the boundary of the anti de Sitter (AdS) solution. We show that the central charge of the dual CFT is proportional to the mass of the AdS solution. We also study cosmological implications of our massless bi-gravity model.

hep-th↗