Rotating wormholes in Einstein-Dirac-Maxwell theory

Abstract

We consider rotating wormhole solutions in general relativity supported by a complex non-phantom spinor field (which provides a nontrivial spacetime topology) and electromagnetic fields. The solutions are asymmetric, regular, asymptotically flat and carry nonzero total angular momentum. The physical properties of the resulting configurations are completely determined by the values of three input quantities: the throat parameter, the spinor frequency, and the electromagnetic coupling constant. The wormholes connect two identical Minkowski spacetimes possessing in general different masses and global charges.

Figures (6)

• Figure 1: The dimensionless total masses $\bar{M}_\pm$ as functions of the parameter $\bar{\Omega}$ for neutral and charged spinor fields with different values of the coupling constant $\bar{e}$. The solid lines correspond to the rotating systems and the dashed lines -- to the nonrotating configurations. The bold dots correspond to the configurations for which the solutions are displayed in Fig. \ref{['fig_plots_sols']}.
• Figure 2: The ratio of the charges of the configurations to the equatorial radius of their throat $\bar{Q}_\pm/\bar{R}_{e}$ (left panel) and the equatorial radius $\bar{R}_e$ (right panel) as functions of $\bar{\Omega}$ for different values of $\bar{e}$. The solid lines correspond to the rotating systems and the dashed lines -- to the nonrotating configurations. 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 $\bar{\Omega}=\bar{\Omega}_{\text{crit}}$: the upper parts of the curves correspond to the charge $\bar{Q}_+$, and the lower parts -- to the charge $\bar{Q}_-$.
• Figure 3: The angular velocity of the throat, $\bar{\omega}_{e}$, versus the rotational velocity of the throat, $\bar{v}_e$, in the equatorial plane. The graphs for $\bar{e}=0$ and $\bar{e}=-0.15$ practically coincide.
• Figure 4: Solutions for the system with the coupling constant $\bar{e}=0$, the throat parameter $x_0=0.2$, and the spinor frequency $\bar{\Omega}=-0.9$ near the center of the configuration. The different rows show: the metric components $g_{tt}, g_{rr}$, and $g_{t\varphi}$; the total energy density $\bar{T}_t^t$, the angular momentum density $\bar{T}_\varphi^t$ (physical component), and the spinor field density $\psi^\dagger\psi$; equipotential lines for the energy density, the angular momentum density, and the spinor field density in the subspace with $x>0$; electric, $\bar{\phi}$, and magnetic, $\bar{\sigma}$, potentials. The yellow surfaces correspond to the solutions in the subspace with $x>0$, and the blue ones -- in the subspace with $x<0$. The throat in the equatorial plane ($\theta=\pi/2$) is located in the subspace with $x<0$ at $u_e\approx 0.2$.
• Figure 5: Lines of force of the dimensionless electric, $\mathbf{\bar{E}}\equiv\sqrt{4\pi G}/m_s \mathbf{E}$, and magnetic, $\mathbf{\bar{H}}\equiv\sqrt{4\pi G}/m_s \mathbf{H}$, fields. The top plots correspond to the subspace with $x>0$, and the bottom plots -- to the subspace with $x<0$.