AI 中文总结
该研究在迹耦合引力中构建了外域精确史瓦西的C∞紧支可穿越虫洞，推导了各向异性源的物质反演公式，局域化了奇异性并给出了参数空间的分支特性。
AI 中文摘要
我们研究作用量密度为f(R,T)=R+λT²的迹耦合引力中的静态球对称可穿越虫洞。该时空由史瓦西时空的C∞形变构建，在有限核外完全消失，因此外域为精确史瓦西时空，无需薄壳或连接面。由于f_R=1，度规方程保持二阶，物质问题简化为局域代数重构。对于各向异性源，我们推导了用有效源和无量纲迹变量χ=λT/(4π)表示的(ρ,p_r,p_t)的统一反演公式，并证明可容许物质分支是三次方程的真空连通实根。所得参数空间包含规则的正密度和负密度喉道区域、重构退化的临界边界以及不可容许的分支失效区。几何本身与分支无关，但重构物质依赖于物质拉格朗日量的规定。在可容许分支上，径向零能量条件（NEC）在喉道处仍不满足，因此该模型仅局域化了奇异性而非消除它。里奇支集和重构物质仍限制在有限区间内，而外域潮汐场为具有ADM质量M的精确史瓦西场。这些结果应被视为所展示的近似族内的可控存在性和可行性陈述，而非稳定性证明。
英文摘要
We study static, spherically symmetric traversable wormholes in trace-coupled gravity with action density f(R,T) = R + lambda T^2. The spacetime is built from C-infinity deformations of Schwarzschild that vanish identically outside a finite core, so the exterior is exactly Schwarzschild and no thin shell or junction surface is needed. Because f_R = 1, the metric equations remain second order and the matter problem reduces to a local algebraic reconstruction. For an anisotropic source, we derive unified inversion formulas for (rho, p_r, p_t) in terms of the effective source and the dimensionless trace variable chi = lambda T/(4 pi), and show that the admissible matter branch is the vacuum-connected real root of a cubic equation. The resulting parameter space contains regular positive-density and negative-density throat regimes, a critical boundary where the reconstruction degenerates, and a nonadmissible branch-failure sector. The geometry itself is branch-independent, but the reconstructed matter depends on the matter-Lagrangian prescription. On the admissible branch the radial NEC still fails at the throat, so the model localizes exoticity rather than removing it. The Ricci support and reconstructed matter remain confined to a finite interval, while the exterior tidal field is exactly Schwarzschild with ADM mass M. The results should be read as controlled existence and viability statements within the displayed ansatz families, not as a stability proof.
Comments15 pages, 10 figures
