从非线性狄拉克系统中涌现的Kastor-Traschen时空
Emergence of Kastor-Traschen spacetime from a nonlinear Dirac system
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中文总结 AI 辅助
该研究在四维时空中证明非线性狄拉克旋量系统可唯一约束背景为Kastor-Traschen动态多黑洞时空，揭示宇宙学常数与黑洞构型从费米子凝聚自发涌现的新几何机制。
中文摘要 AI 辅助
我们在四维时空中建立了一个唯一性定理，证明非线性旋量系统会自然将背景几何约束为Kastor-Traschen时空——该时空描述动态的宇宙多黑洞构型。通过分析一个非线性场方程（其中狄拉克旋量的超协变导数由内禀费米子流提供源项），我们在两个物理要求下评估其可积性：一是保证实厄米积$\bar{\boldsymbol{\text{ψ}}}_R \boldsymbol{\text{ψ}}_L$的锁相条件，二是纯电源条件。我们证明，该场方程唯一地迫使旋量成为超协变狄拉克算符的本征矢，其本征值被动态认定为德西特背景的哈勃常数。这些结果提供了一种全新的几何机制，其中宇宙学常数和动态黑洞构型都从费米子凝聚体中自发涌现。
英文摘要
We establish a uniqueness theorem in four-dimensional spacetime, demonstrating that a nonlinear spinor system naturally constrains the background geometry to the Kastor-Traschen spacetime, which describes dynamical, cosmic multi-black-holes. By analyzing a nonlinear field equation where the super-covariant derivative of a Dirac spinor is sourced by intrinsic fermion currents, we evaluate its integrability under two physical requirements: a phase-locking condition enforcing a real hermitian product $\overlineψ_R ψ_L$, and a pure-electric source condition. We show that the field equation uniquely compels the spinor to be an eigenvector of the super-covariant Dirac operator, with the eigenvalue dynamically identified as the Hubble constant of the de Sitter background. These results provide a novel geometric mechanism wherein both the cosmological constant and dynamical black hole configurations spontaneously emerge from fermion condensates.
