Pub Date : 2023-10-20DOI: 10.1142/s0219887824500749
Shahroud Azami
{"title":"Differential Harnack Inequality for the Newell-Whitehead-Segel Equation Under Finsler-Geometric Flow","authors":"Shahroud Azami","doi":"10.1142/s0219887824500749","DOIUrl":"https://doi.org/10.1142/s0219887824500749","url":null,"abstract":"","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"61 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135568128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1142/s0219887824500609
Bhupendra Kumar Shukla, R. K. Tiwari, A. Beesham, D. Sofuoglu
In this study, we consider the Bianchi type I model in the framework of [Formula: see text] gravity theory. We solve the field equations with the help of an anisotropy parameter that can show the anisotropic behavior of the universe in the past and its approximation to isotropy today. For two different models, we examine the phase transition in the expansion of the universe by analyzing some cosmologic parameters. We conduct our investigation by applying the Markov Chain Monte-Carlo analysis and Bayesian technique to the Cosmic Chronometer, Phanteon and BAO datasets, taking into account the observational constraints on the parameters. We show that the two different models we obtained explain the transition from the slowing phase to the accelerating phase in the expansion of the universe, that the models behave in harmony with the [Formula: see text]CDM model today, and that the current values of the cosmological parameters predicted by the models are compatible with the values indicated by the observations and we conclude that the Model-I is more compatible than the Model-II in this conformity.
{"title":"Cosmology with the late time isotropy of the Bianchi type I model in <i>f</i>(<i>R, T</i>) theory","authors":"Bhupendra Kumar Shukla, R. K. Tiwari, A. Beesham, D. Sofuoglu","doi":"10.1142/s0219887824500609","DOIUrl":"https://doi.org/10.1142/s0219887824500609","url":null,"abstract":"In this study, we consider the Bianchi type I model in the framework of [Formula: see text] gravity theory. We solve the field equations with the help of an anisotropy parameter that can show the anisotropic behavior of the universe in the past and its approximation to isotropy today. For two different models, we examine the phase transition in the expansion of the universe by analyzing some cosmologic parameters. We conduct our investigation by applying the Markov Chain Monte-Carlo analysis and Bayesian technique to the Cosmic Chronometer, Phanteon and BAO datasets, taking into account the observational constraints on the parameters. We show that the two different models we obtained explain the transition from the slowing phase to the accelerating phase in the expansion of the universe, that the models behave in harmony with the [Formula: see text]CDM model today, and that the current values of the cosmological parameters predicted by the models are compatible with the values indicated by the observations and we conclude that the Model-I is more compatible than the Model-II in this conformity.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"8 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514302","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1142/s021988782450049x
Bilender P. Allahverdiev, Huseyin Tuna, Hamlet A. Isayev
In this paper, the Titchmarsh–Weyl theory of the impulsive [Formula: see text]-Dirac equation is studied.
本文研究了脉冲[公式:见文]-狄拉克方程的Titchmarsh-Weyl理论。
{"title":"Titchmarsh-Weyl theory for impulsive <i>q</i>-Dirac equation","authors":"Bilender P. Allahverdiev, Huseyin Tuna, Hamlet A. Isayev","doi":"10.1142/s021988782450049x","DOIUrl":"https://doi.org/10.1142/s021988782450049x","url":null,"abstract":"In this paper, the Titchmarsh–Weyl theory of the impulsive [Formula: see text]-Dirac equation is studied.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514099","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1142/s0219887824400024
Arpan Sardar, Uday Chand De
In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type [Formula: see text], [Formula: see text] or [Formula: see text] and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes.
{"title":"Characterizations of <i>GRW</i> spacetimes admitting Ricci-Yamabe solitons","authors":"Arpan Sardar, Uday Chand De","doi":"10.1142/s0219887824400024","DOIUrl":"https://doi.org/10.1142/s0219887824400024","url":null,"abstract":"In this paper, we investigate Ricci–Yamabe solitons (RYSs) and gradient Ricci–Yamabe solitons (gradient RYSs) in generalized Robertson–Walker (GRW) spacetimes. At first, we prove that if a GRW spacetime admits a RYS, then it becomes a perfect fluid spacetime (PFS) and the divergence of the Weyl tensor vanishes. Also, a GRW spacetime admitting a RYS is of Petrov type [Formula: see text], [Formula: see text] or [Formula: see text] and in case of four dimension, the spacetime turns into a Robertson–Walker spacetime. Next, we show that if a GRW spacetime of constant scalar curvature admits a gradient RYS, then it becomes a PFS and the divergence of the Weyl tensor vanishes.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514280","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1142/s0219887824500750
Changpeng Pan, Zhenghan Shen, Pan Zhang
In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over K"ahler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan--eshadri filtration of the initial twisted Higgs bundle.
{"title":"The Limit of the Yang-Mills-Higgs Flow for twisted Higgs pairs","authors":"Changpeng Pan, Zhenghan Shen, Pan Zhang","doi":"10.1142/s0219887824500750","DOIUrl":"https://doi.org/10.1142/s0219887824500750","url":null,"abstract":"In this paper, we consider the Yang-Mills-Higgs flow for twisted Higgs pairs over K\"ahler manifolds. We prove that this flow converges to a reflexive twisted Higgs sheaf outside a closed subset of codimension $4$, and the limiting twisted Higgs sheaf is isomorphic to the double dual of the graded twisted Higgs sheaves associated to the Harder-Narasimhan--eshadri filtration of the initial twisted Higgs bundle.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135567048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-20DOI: 10.1142/s0219887824500488
Jonatan Herrera, Martin De la Rosa, Rafael M. Rubio
In this work, we consider geometrical models describing spinning particles in the context of generalized Robertson–Walker spacetimes. We study spacelike and timelike trajectories for massive and massless particles governed by two different Lagrangians: one depending on the torsion and the other on the curvature of the trajectory. For both, we are able to relate the curvature and torsion of such trajectories with the curvature of the spatial fiber of the cosmological model. Moreover, several conserved quantities are described as well as their possible relations with physical parameters of the particle.
{"title":"On the geometry and dynamics of relativistic particles in generalized Robertson-Walker spacetimes","authors":"Jonatan Herrera, Martin De la Rosa, Rafael M. Rubio","doi":"10.1142/s0219887824500488","DOIUrl":"https://doi.org/10.1142/s0219887824500488","url":null,"abstract":"In this work, we consider geometrical models describing spinning particles in the context of generalized Robertson–Walker spacetimes. We study spacelike and timelike trajectories for massive and massless particles governed by two different Lagrangians: one depending on the torsion and the other on the curvature of the trajectory. For both, we are able to relate the curvature and torsion of such trajectories with the curvature of the spatial fiber of the cosmological model. Moreover, several conserved quantities are described as well as their possible relations with physical parameters of the particle.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135514098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-18DOI: 10.1142/s0219887824500506
Gopal Sardar, Subenoy Chakraborty
In this paper, we consider two modified Chevallier–Polarski–Linder (CPL) models in the background of homogeneous and isotropic FLRW space-time model. From the observational dataset (Pantheon + BAO + HST) we find that the logarithmic form of the equation of state for the dark energy (model II) is more preferred with the use of AIC and BIC and tightly constrained than the other form of the equation of state parameter (model I). However, model I is more favored compared to the model II in the context of Bayesian evidence. Finally, for [Formula: see text] tension it is found that model I is more preferable than model II.
本文在均匀和各向同性FLRW时空模型的背景下，研究了两种改进的Chevallier-Polarski-Linder (CPL)模型。从观测数据集(Pantheon + BAO + HST)中，我们发现暗能量状态方程的对数形式(模型II)在使用AIC和BIC时比其他形式的状态方程参数(模型I)更受青睐，并且在贝叶斯证据的背景下，模型I比模型II更受青睐。最后，对于[公式:见文]张力，发现模型I比模型II更可取。
{"title":"Observational constraints on modified CPL models for dark energy","authors":"Gopal Sardar, Subenoy Chakraborty","doi":"10.1142/s0219887824500506","DOIUrl":"https://doi.org/10.1142/s0219887824500506","url":null,"abstract":"In this paper, we consider two modified Chevallier–Polarski–Linder (CPL) models in the background of homogeneous and isotropic FLRW space-time model. From the observational dataset (Pantheon + BAO + HST) we find that the logarithmic form of the equation of state for the dark energy (model II) is more preferred with the use of AIC and BIC and tightly constrained than the other form of the equation of state parameter (model I). However, model I is more favored compared to the model II in the context of Bayesian evidence. Finally, for [Formula: see text] tension it is found that model I is more preferable than model II.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1142/s021988782450052x
Juan D. Garcia-Munoz, A. Raya
A relation between classical electrostatic fields and Shrödinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the electrostatic potential as the natural logarithm of a nodeless function, it is demonstrated that the electrostatic fields fulfil the Bernoulli equation associated to a second-order confluent supersymmetric transformation. By using the so-called confluent algorithm, it is possible, given a charge density, to find the corresponding electrostatic field as well as the supersymmetric potentials. Furthermore, the associated charge density and the electrostatic field profile of Schrödinger-like solvable potentials can be determined.
{"title":"Supersymmetric Quantum Potentials Analogs of Classical Electrostatic Fields","authors":"Juan D. Garcia-Munoz, A. Raya","doi":"10.1142/s021988782450052x","DOIUrl":"https://doi.org/10.1142/s021988782450052x","url":null,"abstract":"A relation between classical electrostatic fields and Shrödinger-like Hamiltonians is evidenced. Hence, supersymmetric quantum potentials analogous to classical electrostatic fields can be constructed. Proposing an ansatz for the electrostatic potential as the natural logarithm of a nodeless function, it is demonstrated that the electrostatic fields fulfil the Bernoulli equation associated to a second-order confluent supersymmetric transformation. By using the so-called confluent algorithm, it is possible, given a charge density, to find the corresponding electrostatic field as well as the supersymmetric potentials. Furthermore, the associated charge density and the electrostatic field profile of Schrödinger-like solvable potentials can be determined.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"78 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944965","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1142/s0219887824500464
Manuel Hohmann
In this paper, we study metric teleparallel geometries, which can either be defined through a Lorentzian metric and flat, metric-compatible affine connection, or a tetrad and a flat Lorentz spin connection, which are invariant under the transitive action of a four-dimensional Lie group on their spatial equal-time hypersurfaces. There are three such group actions, and their corresponding spatial hypersurfaces belong to the Bianchi types II, III and IX, respectively. For each of these three symmetry groups, we determine the most general teleparallel geometry, and find that it is parametrized by six functions of time, one of which can be eliminated by the choice of the time coordinate. We further show that these geometries are unique up to global Lorentz transformations, coordinate transformations and changes of the choice of the parameter functions.
{"title":"Spatially homogeneous teleparallel spacetimes with four-dimensional groups of motions","authors":"Manuel Hohmann","doi":"10.1142/s0219887824500464","DOIUrl":"https://doi.org/10.1142/s0219887824500464","url":null,"abstract":"In this paper, we study metric teleparallel geometries, which can either be defined through a Lorentzian metric and flat, metric-compatible affine connection, or a tetrad and a flat Lorentz spin connection, which are invariant under the transitive action of a four-dimensional Lie group on their spatial equal-time hypersurfaces. There are three such group actions, and their corresponding spatial hypersurfaces belong to the Bianchi types II, III and IX, respectively. For each of these three symmetry groups, we determine the most general teleparallel geometry, and find that it is parametrized by six functions of time, one of which can be eliminated by the choice of the time coordinate. We further show that these geometries are unique up to global Lorentz transformations, coordinate transformations and changes of the choice of the parameter functions.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-17DOI: 10.1142/s0219887824500476
Dan Dumitru
The aim of this paper is to study the existence of compact multiply Einstein warped products [Formula: see text], [Formula: see text], [Formula: see text] for every [Formula: see text], [Formula: see text]. We prove the following: (a) [Formula: see text] where [Formula: see text] is the Einstein constant of [Formula: see text], (b) [Formula: see text] where [Formula: see text] is the Einstein constant of [Formula: see text] for every [Formula: see text], (c) [Formula: see text] and [Formula: see text] for every [Formula: see text], (d) [Formula: see text] for equal warping functions.
{"title":"Some remarks on the existence of compact multiply Einstein warped products","authors":"Dan Dumitru","doi":"10.1142/s0219887824500476","DOIUrl":"https://doi.org/10.1142/s0219887824500476","url":null,"abstract":"The aim of this paper is to study the existence of compact multiply Einstein warped products [Formula: see text], [Formula: see text], [Formula: see text] for every [Formula: see text], [Formula: see text]. We prove the following: (a) [Formula: see text] where [Formula: see text] is the Einstein constant of [Formula: see text], (b) [Formula: see text] where [Formula: see text] is the Einstein constant of [Formula: see text] for every [Formula: see text], (c) [Formula: see text] and [Formula: see text] for every [Formula: see text], (d) [Formula: see text] for equal warping functions.","PeriodicalId":50320,"journal":{"name":"International Journal of Geometric Methods in Modern Physics","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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