AI 中文总结
该研究在线性遥平行高斯-博内特引力中构建解析厚膜解，通过推导解析分裂条件与张量稳定性要求确定可行参数区域，表明张量谱无快子不稳定性且支持引力子零模，大量子扇区有引力共振，建立了膜分裂、张量稳定性和引力共振的联系。
AI 中文摘要
我们使用由正弦-戈登超势产生的一阶形式，在线性遥平行高斯-博内特引力中构建了一个解析厚膜解。所得的渐近\(\mathrm{AdS}_5\)构型表现出由无量纲参数\(q = 4\alpha k^2\)控制的膜分裂。推导了一个解析分裂条件，并与张量稳定性要求相结合，以确定物理上可行的参数区域。我们表明张量谱没有快子不稳定性，并支持一个可归一化的引力子零模。大量子扇区表现出奇宇称引力共振，其准定域性在稳定性边界附近显著增强。我们的结果在遥平行高斯-博内特膜世界中的膜分裂、张量稳定性和引力共振之间建立了直接联系。
英文摘要
We construct an analytical thick-brane solution in linear teleparallel Gauss-Bonnet gravity using a first-order formalism generated by a sine-Gordon superpotential. The resulting asymptotically $\mathrm{AdS}_5$ configurations exhibit brane splitting controlled by the dimensionless parameter $q=4αk^2$. An analytical splitting condition is derived and combined with tensor-stability requirements to identify the physically viable parameter region. We show that the tensor spectrum is free of tachyonic instabilities and supports a normalizable graviton zero mode. The massive sector exhibits odd-parity gravitational resonances whose quasi-localization is significantly enhanced near the stability boundary. Our results establish a direct link between brane splitting, tensor stability, and gravitational resonances in teleparallel Gauss-Bonnet braneworlds.
Comments8 pages, 4 captioned figures, and 2 tables. To appear in Europhysics Letters
