In previous work, we analyzed the linear and nonlinear stability of static, spherically symmetric wormhole solutions to Einsteins field equations coupled to a massless ghost scalar field. Our analysis revealed that all these solutions are unstable wi
th respect to linear and nonlinear spherically symmetric perturbations and showed that the perturbation causes the wormholes to either decay to a Schwarzschild black hole or undergo a rapid expansion. Here, we consider charged generalization of the previous models by adding to the gravitational and ghost scalar field an electromagnetic one. We first derive the most general static, spherically symmetric wormholes in this theory and show that they give rise to a four-parameter family of solutions. This family can be naturally divided into subcritical, critical and supercritical solutions depending on the sign of the sum of the asymptotic masses. Then, we analyze the linear stability of these solutions. We prove that all subcritical and all critical solutions possess one exponentially in time growing mode. It follows that all subcritical and critical wormholes are linearly unstable. In the supercritical case we provide numerical evidence for the existence of a similar unstable mode.
We analyze the nonlinear evolution of spherically symmetric wormhole solutions coupled to a massless ghost scalar field using numerical methods. In a previous article we have shown that static wormholes with these properties are unstable with respect
to linear perturbations. Here we show that depending on the initial perturbation the wormholes either expand or decay to a Schwarzschild black hole. We estimate the time scale of the expanding solutions and the ones collapsing to a black hole and show that they are consistent in the regime of small perturbations with those predicted from perturbation theory. In the collapsing case, we also present a systematic study of the final black hole horizon and discuss the possibility for a luminous signal to travel from one universe to the other and back before the black hole forms. In the expanding case, the wormholes seem to undergo an exponential expansion, at least during the run time of our simulations.
We examine the linear stability of static, spherically symmetric wormhole solutions of Einsteins field equations coupled to a massless ghost scalar field. These solutions are parametrized by the areal radius of their throat and the product of the mas
ses at their asymptotically flat ends. We prove that all these solutions are unstable with respect to linear fluctuations and possess precisely one unstable, exponentially in time growing mode. The associated time scale is shown to be of the order of the wormhole throat divided by the speed of light. The nonlinear evolution is analyzed in a subsequent article.
We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] times Sigma$, where $Sigma$ is a compact manifold with smooth boundaries $partialSigma$. By using an appropriate reduction to a fir
st order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on $partialSigma$. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwells equations in the Lorentz gauge and Einsteins gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.
We examine the dynamical behavior of recently introduced bubbles in asymptotically flat, five-dimensional spacetimes. Using numerical methods, we find that even bubbles that initially start expanding eventually collapse to a Schwarzschild-Tangherlini black hole.
