标题： 爱因斯坦-玻恩-英菲尔德-矢量模型中的自发矢量化 显示英文标题

标题： Spontaneous Vectorization in the Einstein-Born-Infeld-Vector Model

摘要： 我们研究爱因斯坦-玻恩-英费尔德-矢量（EBIV）模型中的自发矢量化，其中无质量的矢量场非最小地耦合到非线性的玻恩-英费尔德（BI）电磁场。这种耦合导致在玻恩-英费尔德黑洞（BIBH）背景中矢量场获得有效质量，引发超光速不稳定性。我们数值构建并分析此类矢量化玻恩-英费尔德黑洞（VBIBHs），重点关注它们的存在域、热力学性质以及在类似瑞斯纳-诺德斯特伦（RN）和类似施瓦茨希尔德背景中的能量分布。在类似RN的BI背景中，矢量化解从微扰不稳定性阈值出现，并持续到极端情况，与未矢化的对应解相比，表现出更高的熵和更低的自由能。相反，在类似施瓦茨希尔德的背景下，VBIBHs表现出分叉行为，存在两个共存的解分支，其中仅有一个在热力学上占优。我们揭示了两种情况下内部和外部场之间的能量重新分布模式的对比，这由矢量场和非线性BI场之间的竞争所主导。我们的发现突显了非线性电动力学中自发矢化的丰富结构，并为超越线性麦克斯韦理论的黑洞物理提供了新的见解。 显示英文摘要

摘要： We investigate spontaneous vectorization in the Einstein-Born-Infeld-Vector (EBIV) model, where a massless vector field is nonminimally coupled to a nonlinear Born-Infeld (BI) electromagnetic field. This coupling results in an effective mass for the vector field in a Born-Infeld black hole (BIBH) background, triggering tachyonic instability. We numerically construct and analyze such vectorized Born-Infeld black holes (VBIBHs), focusing on their domain of existence, thermodynamic properties, and energy distributions in both Reissner-Nordstr\"om (RN)-like and Schwarzschild-like backgrounds. In RN-like BI backgrounds, vectorized solutions emerge from the perturbative instability threshold and persist down to extremality, exhibiting higher entropy and lower free energy compared to their unvectorized counterparts. Conversely, in Schwarzschild-like backgrounds, VBIBHs show bifurcation behavior with two coexisting solution branches, only one of which is thermodynamically favored. We reveal a contrasting energy redistribution pattern between the internal and external fields in the two regimes, governed by the competition between the vector field and the nonlinear BI field. Our findings highlight the rich structure of spontaneous vectorization in nonlinear electrodynamics and provide novel insights into black hole physics beyond linear Maxwell theory.