Charged wormholes can be long-lived

Abstract

Ellis-Bronnikov wormholes suffer from an unstable radial mode. Here we investigate the evolution of the unstable mode(s) for charged wormholes. We show that the instability remains in the presence of charge, but exhibits a very fast decrease to zero, suggesting that wormholes that approach a near-extremal metric could be long-lived. For so-called supercritical wormholes, two purely imaginary unstable modes merge and continue with degenerate imaginary parts and opposite real parts. By analogy, we conjecture an analogous behavior for rotating wormholes.

Figures (3)

• Figure 1: Domain of existence of the electrically charged wormholes: The brown shaded area corresponds to supercritical wormholes, while the green shaded area corresponds to the subcritical wormholes. They are separated by the critical wormholes (black line). Other colored curves correspond to families of solutions with fixed values of the parameters. All the curves terminate at the extremal Reissner-Nordström black hole (eRN).
• Figure 2: Unstable radial modes of subcritical and critical wormholes. The inset shows the critical wormhole decay time $\tau_0$ as a function of the mass $M$, and a fit (dashed line) described by (\ref{['num_rel']}).
• Figure 3: Unstable radial modes of supercritical and critical wormholes.