标题： 半经典虫洞几何中的迹异常贡献 显示英文标题

标题： Trace anomaly contributions to semi-classical wormhole geometries

摘要： 我们研究在共形异常（或迹异常）存在的情况下，半经典爱因斯坦方程框架内的虫洞解。这些解由来自迹异常的应力-能量张量（SET）源产生，并依赖于两个由理论物质内容和涉及量子场的自由度决定的正系数，$\alpha$和$\lambda$。对于类型 B 的异常（$\alpha=0$），我们假设一个常数红移函数，得到虫洞几何结构，并表明 SET 成分随着参数$\lambda$增加。在类型 A 异常（$\lambda=0$）的情况下，我们推广了之前已知的解，得出一个包括类时虫洞、裸奇点和施瓦茨希尔德黑洞的几何家族。使用各向同性坐标，我们确定产生可穿越虫洞解的参数选择。扩展到完整的迹异常贡献，我们在喉部附近求解微分方程以获得红移函数，并证明在喉部处里奇标量和克雷茨曼标量保持有限。我们进一步分析了光子和类时粒子的轨迹，表明光子测地线的有效势的高度和宽度随着$\alpha$单调增加，而最内稳定圆轨道（ISCO）半径也随着更大的$\alpha$而增大。这些结果展示了迹异常效应与虫洞时空结构和动力学之间的丰富相互作用。 显示英文摘要

摘要： We investigate wormhole solutions within the framework of the semi-classical Einstein equations in the presence of the conformal anomaly (or trace anomaly). These solutions are sourced by a stress-energy tensor (SET) derived from the trace anomaly, and depend on two positive coefficients, $\alpha$ and $\lambda$, determined by the matter content of the theory and on the degrees of freedom of the involved quantum fields. For a Type B anomaly ($\alpha=0$), we obtain wormhole geometries assuming a constant redshift function and show that the SET components increase with the parameter $\lambda$. In the case of a Type A anomaly ($\lambda=0$), we generalize previously known solutions, yielding a family of geometries that includes Lorentzian wormholes, naked singularities, and the Schwarzschild black hole. Using isotropic coordinates, we identify parameter choices that produce traversable wormhole solutions. Extending to the full trace-anomaly contribution, we solve the differential equation near the throat to obtain the redshift function and demonstrate that both the Ricci and Kretschmann scalars remain finite at the throat. We further analyze the trajectories of null and timelike particles, showing that the height and width of the effective potential for null geodesics increase monotonically with $\alpha$, while the innermost stable circular orbit (ISCO) radius also grows with larger $\alpha$. These results illustrate the rich interplay between trace anomaly effects and the structure and dynamics of wormhole spacetimes.