发表机构
Universidade Federal da Paraíba（帕拉伊巴联邦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究洛伦兹破缺Kalb-Ramond引力中带里奇与黎曼张量非最小耦合的均匀哥德尔型几何，推导相关方程，分析伪磁场背景下的耦合效应及闭合类时曲线临界半径，讨论各类物质源的情况。
AI 中文摘要
本文研究引力模型中的均匀哥德尔型几何，该模型中局域洛伦兹对称性由反对称Kalb-Ramond二阶张量的真空期望值自发破缺。我们考虑爱因斯坦-希尔伯特作用量，其补充了两个独立的非最小曲率耦合：形式为$B_{a}{}^{c}B_{bc}R^{ab}$的里奇张量耦合，以及形式为$B^{ab}B^{cd}R_{abcd}$的黎曼张量耦合。在均匀真空区域，即Kalb-Ramond场强和对称性破缺势的一阶导数均为零的情况下，场方程在哥德尔型度规的标架下约化为一个封闭代数系统。我们针对真空二阶张量的几种不等价取向推导了曲率张量、约化度规方程和Kalb-Ramond一致性方程。特别关注伪磁场背景$B_{12}=b$，因为它保留了旋转平面的对称性，且给出了对常规bumblebee结果的清晰变形。对于该区域，Kalb-Ramond方程确定$\frac{m^2}{\rho^2}=\frac{2(\rho_1+3\rho_2)}{\rho_1+2\rho_2}$，其中$\rho_1$和$\rho_2$分别为里奇耦合和黎曼耦合。仅里奇耦合会产生非因果的哥德尔值$m^2=2\rho^2$，而黎曼耦合会改变时序边界，当$\rho_2=-\rho_1$时可得到临界因果值$m^2=4\rho^2$。我们还表明，黎曼耦合可移动闭合类时曲线的临界半径，但普通正能物质对完全因果解有严格限制。最后，我们讨论了理想流体、标量场和电磁源。
英文摘要
This paper studies homogeneous \Godel-type geometries in a gravitational model where local Lorentz symmetry is spontaneously broken by the vacuum expectation value of an antisymmetric Kalb-Ramond two-form. We consider the Einstein-Hilbert action supplemented by two independent nonminimal curvature couplings: a Ricci-tensor coupling of the form $B_{a}{}^{c}B_{bc}R^{ab}$ and a Riemann-tensor coupling of the form $B^{ab}B^{cd}R_{abcd}$. In the homogeneous vacuum sector, where the Kalb-Ramond field strength and the first derivatives of the symmetry-breaking potential vanish, the field equations reduce to a closed algebraic system in the tetrad frame of the \Godel-type metric. We derive the curvature tensors, the reduced metric equations, and the Kalb-Ramond consistency equations for several inequivalent orientations of the vacuum two-form. Particular attention is given to the pseudo-magnetic background $B_{12}=b$, because it preserves the symmetry of the rotation plane and yields a transparent deformation of the usual bumblebee result. For this sector the Kalb-Ramond equation fixes $\frac{m^2}{ω^2}=\frac{2(ξ_1+3ξ_2)}{ξ_1+2ξ_2}$, where $ξ_1$ and $ξ_2$ are the Ricci and Riemann couplings. The Ricci coupling alone reproduces the noncausal \Godel value $m^2=2ω^2$, while the Riemann coupling shifts the chronology bound and allows the critical causal value $m^2=4ω^2$ for $ξ_2=-ξ_1$. We also show that the Riemann coupling can move the critical radius for closed timelike curves, but ordinary positive-energy matter severely restricts completely causal solutions. Finally, we discuss perfect fluid, scalar field, and electromagnetic sources.
Comments21 pages
