Symmetry Calculation and Cartan Geometry of Melvin Space-time

IF 1.1 3区物理与天体物理 Q3 PHYSICS, MULTIDISCIPLINARY

Foundations of Physics Pub Date : 2025-10-23 DOI:10.1007/s10701-025-00892-9

Rohollah Bakhshandeh-Chamazkoti, Yaser Kord

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Abstract

This study investigates the Noether symmetries and geometric properties of the Melvin magnetic spacetime, focusing on the associated first integrals and conservation laws. The analysis begins with a detailed examination of the Noether symmetries, identifying the corresponding infinitesimal generators and their commutation relations. These symmetries yield first integrals that are crucial for understanding the dynamical properties of the spacetime, including Lagrangian invariance, angular momentum, generalized momentum, energy, and linear momentum along the z-axis. The study further delves into the geometric structure of the spacetime, using the vielbein formalism and Cartan structure equations to describe the underlying spin connections. Finally, perturbation and stability analysis is conducted on the effective potential governing the motion of a test particle, comparing unperturbed and perturbed potentials to explore the impact of metric perturbations on the stability of circular orbits. The results provide valuable insights into the stability characteristics of the Melvin magnetic spacetime under small perturbations.

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梅尔文时空的对称计算与卡坦几何

本文研究了梅尔文磁时空的诺特对称性和几何性质，重点研究了相关的第一积分和守恒定律。分析开始于对诺特对称的详细检查，确定相应的无穷小发生器及其交换关系。这些对称性产生的第一积分对于理解时空的动力学特性至关重要，包括拉格朗日不变性、角动量、广义动量、能量和沿z轴的线性动量。本研究进一步探讨了时空的几何结构，使用维埃尔拜因形式和卡坦结构方程来描述潜在的自旋连接。最后，对控制测试粒子运动的有效势进行摄动和稳定性分析，比较无摄动和摄动势，探讨度量摄动对圆轨道稳定性的影响。这些结果为研究梅尔文磁时空在小扰动下的稳定性特性提供了有价值的见解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Foundations of Physics 物理-物理：综合

CiteScore

2.70

自引率

6.70%

发文量

104

审稿时长

6-12 weeks

期刊介绍： The conceptual foundations of physics have been under constant revision from the outset, and remain so today. Discussion of foundational issues has always been a major source of progress in science, on a par with empirical knowledge and mathematics. Examples include the debates on the nature of space and time involving Newton and later Einstein; on the nature of heat and of energy; on irreversibility and probability due to Boltzmann; on the nature of matter and observation measurement during the early days of quantum theory; on the meaning of renormalisation, and many others. Today, insightful reflection on the conceptual structure utilised in our efforts to understand the physical world is of particular value, given the serious unsolved problems that are likely to demand, once again, modifications of the grammar of our scientific description of the physical world. The quantum properties of gravity, the nature of measurement in quantum mechanics, the primary source of irreversibility, the role of information in physics – all these are examples of questions about which science is still confused and whose solution may well demand more than skilled mathematics and new experiments. Foundations of Physics is a privileged forum for discussing such foundational issues, open to physicists, cosmologists, philosophers and mathematicians. It is devoted to the conceptual bases of the fundamental theories of physics and cosmology, to their logical, methodological, and philosophical premises. The journal welcomes papers on issues such as the foundations of special and general relativity, quantum theory, classical and quantum field theory, quantum gravity, unified theories, thermodynamics, statistical mechanics, cosmology, and similar.