{"title":"Bound-state solutions for the charged Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime","authors":"R. R. S. Oliveira","doi":"10.1007/s10714-025-03447-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in <span>\\((2+1)\\)</span>-dimensions, where such solutions are given by the two-component normalizable Dirac spinor and by the relativistic energy spectrum. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). After solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers <i>n</i> and <span>\\(m_j\\)</span>, and depends on the angular frequency <span>\\(\\omega \\)</span> (describes the DO), cyclotron frequency <span>\\(\\omega _c\\)</span> (describes the external magnetic field), angular velocity <span>\\(\\Omega \\)</span> (describes the rotating frame), spin parameter <i>s</i> (describes the “spin”), spinorial parameter <i>u</i> (describes the components of the spinor), effective rest mass <span>\\(m_{eff}\\)</span> (describes the rest mass modified by the spin-rotation coupling), and on a real parameter <span>\\(\\sigma \\)</span> and cosmological constant <span>\\(\\Lambda \\)</span> (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to <span>\\(\\Omega \\)</span>) and has its degeneracy broken (due to <span>\\(\\sigma \\)</span> and <span>\\(\\Lambda \\)</span>). Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of <i>n</i> and <span>\\(m_j\\)</span>.</p></div>","PeriodicalId":578,"journal":{"name":"General Relativity and Gravitation","volume":"57 7","pages":""},"PeriodicalIF":2.8000,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"General Relativity and Gravitation","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s10714-025-03447-5","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we determine the relativistic bound-state solutions for the charged (DO) Dirac oscillator in a rotating frame in the Bonnor-Melvin-Lambda spacetime in \((2+1)\)-dimensions, where such solutions are given by the two-component normalizable Dirac spinor and by the relativistic energy spectrum. To analytically solve our problem, we consider two approximations, where the first is that the cosmological constant is very small (conical approximation), and the second is that the linear velocity of the rotating frame is much less than the speed of light (slow rotation regime). After solving a second-order differential equation, we obtain a generalized Laguerre equation, whose solutions are the generalized Laguerre polynomials. Consequently, we obtain the energy spectrum, which is quantized in terms of the radial and total magnetic quantum numbers n and \(m_j\), and depends on the angular frequency \(\omega \) (describes the DO), cyclotron frequency \(\omega _c\) (describes the external magnetic field), angular velocity \(\Omega \) (describes the rotating frame), spin parameter s (describes the “spin”), spinorial parameter u (describes the components of the spinor), effective rest mass \(m_{eff}\) (describes the rest mass modified by the spin-rotation coupling), and on a real parameter \(\sigma \) and cosmological constant \(\Lambda \) (describes the Bonnor-Melvin-Lambda spacetime). In particular, we note that this spectrum is asymmetrical (due to \(\Omega \)) and has its degeneracy broken (due to \(\sigma \) and \(\Lambda \)). Besides, we also graphically analyze the behavior of the spectrum and of the probability density as a function of the parameters of the system for different values of n and \(m_j\).
期刊介绍:
General Relativity and Gravitation is a journal devoted to all aspects of modern gravitational science, and published under the auspices of the International Society on General Relativity and Gravitation.
It welcomes in particular original articles on the following topics of current research:
Analytical general relativity, including its interface with geometrical analysis
Numerical relativity
Theoretical and observational cosmology
Relativistic astrophysics
Gravitational waves: data analysis, astrophysical sources and detector science
Extensions of general relativity
Supergravity
Gravitational aspects of string theory and its extensions
Quantum gravity: canonical approaches, in particular loop quantum gravity, and path integral approaches, in particular spin foams, Regge calculus and dynamical triangulations
Quantum field theory in curved spacetime
Non-commutative geometry and gravitation
Experimental gravity, in particular tests of general relativity
The journal publishes articles on all theoretical and experimental aspects of modern general relativity and gravitation, as well as book reviews and historical articles of special interest.