发表机构
Centre for Theoretical Physics, The British University; Centre for Space Research, North-West University（英国大学理论物理中心; 西北大学空间研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在宇称破缺四腿引力中研究线性模式与有源辐射，发现矢量模式传播速度依赖耦合且哈密顿量非正定，并推导了八种极化的源振幅关系及能量动量通量。
AI 中文摘要
我们在一个四参数四腿引力理论中研究了线性引力模式、有源远场以及二次能量平衡。该理论包含三个宇称偶数挠率不变量和一个宇称奇数耦合 $v^\mu a_\mu$，其中 $v_\mu$ 和 $a_\mu$ 分别是矢量挠率和轴矢量挠率分量。在闵可夫斯基时空周围线性化并应用标量-矢量-张量分解后，我们在一般的非简并宇称破缺区域发现了两个张量、两个标量和四个矢量自由度。张量和标量模式以光速传播，而两个矢量分支具有依赖于耦合的传播速度。我们推导了它们的动力学本征值、特征速度和通量归一化。一个精确的迹恒等式表明，在一般分支中，矢量哈密顿量不是正定的，即使动力学本征值为正且传播速度为实数。我们还推导了对一般紧致正则源的响应，并获得了所有八个线性极化的显式源到振幅关系。场 $V_\mu=\partial^\nu B_{\nu\mu}$ 被用来说明内禀自旋多极。我们进一步证明了对于所选的一阶导数四腿拉格朗日量，二次诺特流等于二阶 Møller 流，并推导了相应的模式分辨能量和动量通量。由于哈密顿量无界，矢量贡献仍然是一个形式上的有符号响应。静态极限重现了参考文献[ShirafujiNashed1997]的结果，一个代表性的参数扫描说明了矢量模式分裂和动力学简并。
英文摘要
We study linear gravitational modes, sourced far-zone fields, and quadratic energy balance in a four-parameter tetrad theory of gravity. The theory contains three parity-even torsion invariants and a parity-odd coupling $v^μa_μ$, where $v_μ$ and $a_μ$ are the vector and axial torsion components. Linearizing around Minkowski spacetime and applying a scalar--vector--tensor decomposition, we find two tensor, two scalar, and four vector degrees of freedom in the generic nondegenerate parity-violating region. The tensor and scalar modes propagate at the speed of light, while the two vector branches have coupling-dependent propagation speeds. We derive their kinetic eigenvalues, characteristic speeds, and flux normalizations. An exact trace identity shows that the vector Hamiltonian is not positive definite in the generic branch, even when the kinetic eigenvalues are positive and the propagation speeds are real. We also derive the response to a general compact canonical source and obtain explicit source-to-amplitude relations for all eight linear polarizations. The field $V_μ=\partial^νB_{νμ}$ is used to illustrate intrinsic-spin multipoles. {We further prove that the quadratic Noether current equals the second-order Møller current for the chosen first-derivative tetrad Lagrangian and derive the corresponding mode-resolved energy and momentum fluxes.} The vector contribution remains a formal signed response because of the unbounded Hamiltonian. The stationary limit reproduces the results of Ref.~\cite{ShirafujiNashed1997}, and a representative parameter scan illustrates vector-mode splitting and kinetic degeneracy.
Comments20 pages, one figure and four tables
