Trace anomaly contributions to semi-classical wormhole geometries

Abstract

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.