Trace anomaly contributions to semi-classical wormhole geometries

TL;DR

This work shows that trace-anomaly effects in semi-classical gravity can source a wide class of traversable wormholes, with the anomaly-induced SET governed by positive parameters $\alpha$ and $\lambda$. By analyzing Type A ($\lambda=0$), Type B ($\alpha=0$), and the full anomaly, the authors construct geometries ranging from Lorentzian wormholes to naked singularities and Schwarzschild-like spacetimes, ensuring regular curvature at the throat in the general case. They find that curvature invariants $\mathcal{R}$ and $\mathcal{K}$ remain finite at the throat and that the anomaly parameters tune the stress-energy content and the effective potential for null geodesics and the ISCO for timelike geodesics. Overall, the results highlight a robust role for quantum trace anomalies in shaping both the geometry and the dynamics around wormholes, offering a bridge between quantum field theory in curved spacetime and semi-classical gravity with potential observational implications.

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, $α$ and $λ$, determined by the matter content of the theory and on the degrees of freedom of the involved quantum fields. For a Type B anomaly ($α=0$), we obtain wormhole geometries assuming a constant redshift function and show that the SET components increase with the parameter $λ$. In the case of a Type A anomaly ($λ=0$), 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 $α$, while the innermost stable circular orbit (ISCO) radius also grows with larger $α$. These results illustrate the rich interplay between trace anomaly effects and the structure and dynamics of wormhole spacetimes.

Figures (8)

• Figure 1: The behavior of $1-b(r)/r$ with respect to $r$ for $r_0=2$ and $\lambda=0$ (solid red curve), $\lambda=0.5$ (dashed blue curve), respectively.
• Figure 2: The behavior of $\rho +p_{r}$ (top left plot), $\rho +p_{t}$ (top right plot) and $\rho$ (bottom plot) versus $r$. The model parameters have been set as, $r_0=2$. The curves from up to down correspond to the cases with $\lambda=0.01$ (red solid curve), $\lambda=0.3$ (blue dotted curve), $\lambda=0.5$ (green dashed curve) respectively.
• Figure 3: The behavior of $\rho +p_{r}$ (right panel) and $\rho +p_{t}$ (left panel) versus $r$. The model parameters have been set as, $r_0=2$. The solid, dotted and dashed curves correspond to the cases with $\alpha=0,0.03,0.06$ respectively.
• Figure 4: The behavior of $f(r)$ for $\alpha=0.1$ with respect to $r$ for $r_0=2$ and $\lambda=0.01$ (green dashed curve), $\lambda=0.05$ (blue dashed curve), $\lambda= 0.1$ (red solid curve), respectively.
• Figure 5: The behavior of $p_{r}$ (right panel) and $p_{t}$ (left panel) versus $r$. The model parameters have been set as, $r_0=2$ and $\alpha=0.1$. The solid and dotted curves correspond to the cases with $\lambda=0.05, 0.01$ respectively.