Wormholes in Einstein-Dirac-Maxwell theory with identical spacetime asymptotics

TL;DR

This work constructs complete families of regular wormhole solutions in Einstein-Dirac-Maxwell theory using two opposite-spin spinor fields and a Maxwell field that connect two identical Minkowski spacetimes. The configurations are governed by the throat geometry $x_0$, spinor frequency $\bar{\Omega}$, and spinor–Maxwell coupling $\bar{e}$, showing rich behavior including negative ADM masses for $\bar{e}=0$ and extremal Reissner–Nordström-like limits near $\bar{\Omega}_{\mathrm{crit}}\approx -\bar{e}$ when $\bar{e}>0$. The exterior regions approach RN-type metrics with $\bar{Q}_{\pm}/\bar{M}_{\pm}\to 1$ in the appropriate limit, while energy conditions are violated in regions to sustain the topology; stability indicators suggest that energetically stable solutions can exist for the physically allowed range $0\leq \bar{e}<1$. The results advance understanding of wormholes sourced by spinor and electromagnetic fields without thin shells and highlight the interplay between geometry, charges, and stability in asymmetric, two-ended configurations.

Abstract

Within general relativity, we study spherically symmetric configurations with wormhole topology consisting of spinor fields and a Maxwell electric field. For such a system, we construct complete families of regular asymmetric solutions describing wormholes connecting two identical Minkowski spacetimes. The physical properties of such systems are completely determined by the values of three input quantities: the throat parameter, the spinor frequency, and the coupling constant. Depending on the specific values of these parameters, the configurations may have essentially different characteristics, including negative ADM masses.

Figures (6)

• Figure 1: The dimensionless total masses $\bar{M}_\pm$ as functions of the parameter $\bar{\Omega}$ for an uncharged spinor field ($\bar{e}=0$) and different values of $x_0$. As $\bar{\Omega}\to 0$, the masses diverge as $\bar{M}_\pm\sim \bar{\Omega}^{-1}$. The insets show the behavior of the curves in the region $\bar{\Omega}\to -1$.
• Figure 2: The dimensionless circumferential radius of the throat $\bar{R}_{\text{th}}\equiv \mu R_{\text{th}}$ as a function of the parameter $\bar{\Omega}$.
• Figure 3: The dimensionless total masses $\bar{M}_\pm$ as functions of the parameter $\bar{\Omega}$ for a charged spinor field with different values of the coupling constant $\bar{e}$. As $\bar{\Omega}\to \bar{\Omega}_{\text{crit}}\approx -\bar{e}$, the masses diverge, as in the case with $\bar{e}=0$ shown in Fig. \ref{['fig_Mass_Omega_e_0']}. The bold dots correspond to the configurations for which the solutions are displayed in Fig. \ref{['fig_plots_sols']}.
• Figure 4: The ratio of the charges of the configurations to the radius of their throat $\bar{Q}_\pm/\bar{R}_{\text{th}}$ as a function of $\bar{\Omega}$ for different values of $\bar{e}$. For the systems with $\bar{e}= 0$, the charges $\bar{Q}_+$ and $\bar{Q}_-$ are equal, $\bar{Q}_+=\bar{Q}_-= \bar{Q}$. For the systems with $\bar{e}\neq 0$, there are turning points located at $\bar{\Omega}=\bar{\Omega}_{\text{crit}}$ where $\bar{Q}_\pm/\bar{R}_{\text{th}}\to 1$: the upper parts of the curves correspond to the charge $\bar{Q}_+$, and the lower parts -- to the charge $\bar{Q}_-$.
• Figure 5: Typical solutions for different values of the coupling constant $\bar{e}$ for a fixed $x_0=0.2$. The solutions are given for three masses $\bar{M}_+\approx 1, 5, 40$ (the corresponding points in the mass curves for $\bar{M}_\pm$ are shown by bold dots in Fig. \ref{['fig_Mass_Omega_e_neq_0']}). To visualize the results, we have introduced the rescalings $\bar{u}\to \alpha \bar{u}, \bar{v}\to \beta \bar{v}$, and $\bar{\phi}^{\prime 2}\to \gamma \bar{\phi}^{\prime 2}$, where $\alpha=1, 50, 500$, $\beta=1, 5, 50$, $\gamma=1, 100, 1000$ for $\bar{M}_+\approx 1, 5, 40$, respectively.