Dynamical Formation of Charged Wormholes

TL;DR

This work constructs static, charged traversable wormhole solutions supported by negative-energy bidirectional null dust and an electric field, and demonstrates how such wormholes can form dynamically from a Reissner–Nordström black hole by sewing together RN, Vaidya, and wormhole regions with null shells. The authors derive the governing Einstein–Maxwell equations, characterize the throat via the condition $f(r_0)=0$ and $r_0>Q$, and confirm flare-out and NEC violation while showing the spacetime is not asymptotically flat. They extend the construction to charged flux, allowing the shell to carry charge and deriving matching conditions that relate the initial and final charges and masses; the throat radius is then given by $r_0 = M+\Delta M \pm \sqrt{(M+\Delta M)^2 - (Q_{\mathrm{ini}}+\Delta Q)^2}$ with $\Delta Q$ fixed by charge continuity. The analysis highlights how semiclassical negative-energy effects can mediate nontrivial spacetime topologies and provides a controlled dynamical pathway from a familiar BH spacetime to a traversable wormhole, including global causal structure via Barrabès–Israel junctions. Overall, the work clarifies the parameter regimes and energy conditions required for such a transition and sets the stage for further exploration of dynamical, charged wormholes in semiclassical gravity.

Abstract

We construct static, spherically symmetric, charged traversable wormhole solutions to the Einstein--Maxwell equations, supported by bidirectional (ingoing and outgoing) null dust with negative energy, and discuss a scenario for their dynamical formation from a black hole. Our solution contains a traversable throat, where the areal radius takes a minimum, although the spacetime is not asymptotically flat. In our formation scenario, the spacetime evolves sequentially from a black hole to Vaidya regions and finally to a wormhole, with each transition mediated by an impulsive null shell. We find that the radius of the wormhole throat is determined by the mass and charge of the initial black hole as well as those of the injected shell.

Figures (10)

• Figure 1: The Penrose diagram of the traversable wormhole solution. The wavy lines represent curvature singularities, where the areal radius diverges, $r \to \infty$. This spacetime possesses future/past timelike infinities $i^{\pm}$ in the sense that there exist future/past complete timelike geodesics, such as the world line staying at the throat $r = r_{0}$ (shown as the red line).
• Figure 2: A series of symmetric wormhole solutions. The initial conditions for each solution is set as $\hat{A}(0) = r_{0}/Q, \hat{A}'(0) = 10^{-5}, \hat{A}"(0) = 4$. Note that actual throat is located at $\hat{r}_{*} = \mathcal{O}(10^{-6})$.
• Figure 3: Plot of $- g_{tt}$ for a series of symmetric wormhole solutions. All solutions satisfy $- g_{tt} > 0$ throughout the entire domain.
• Figure 4: Relation between $Q$ and $r_{0}$, fixing the asymptotic scale $\bar{r}$. The right edge of the plot approaches to $Q \to 0$ and $r_{0}/\bar{r} \to 0.564 \sim 1/\sqrt{\pi}$, which corresponds to the Hayward's symmetric wormhole solution. There is the upper bound for the charge $Q$, which is given by $Q/\bar{r} \sim 0.191$ with the throat size $r_{0}/\bar{r} \sim 0.403$. This corresponds to the initial condition $r_{0}/Q \sim 2.11$.
• Figure 5: Solutions with the following initial conditions imposed at $\hat{r} = 50$: (i) $(\hat{A}, \hat{A}', \hat{A}")= (\hat{A}_{\text{ext}}, \hat{A}'_{\text{ext}}, \hat{A}"_{\text{ext}})$ (blue), (ii) $(\hat{A}, \hat{A}', \hat{A}") = (\hat{A}_{\text{ext}}, 0.9 *\hat{A}'_{\text{ext}}, \hat{A}"_{\text{ext}})$ (orange), (iii) $(\hat{A}, \hat{A}', \hat{A}") = (\hat{A}_{\text{ext}}, 1.1 *\hat{A}'_{\text{ext}}, \hat{A}"_{\text{ext}})$ (green), where $A_{\text{ext}}$ is the symmetric wormhole solution with the extremal initial condition $r_{0}/Q \sim 2.11$. The origin of $\hat{r}_{*}$ is shifted so that $\hat{r}_{*} = 0$ corresponding $A' = 0$. The orange plot represents asymmetric wormhole, while the green plot cannot be solved beyond $r_{*} = 0$.