Characterizing a class of accelerating wormholes with periodic potential

TL;DR

This paper explores the properties, stability, and topological features of a new class of accelerating wormholes described by the Wormhole C--metric, revealing their potential as horizonless, stable spacetime solutions with unique photon and perturbation characteristics.

Contribution

It characterizes the topological and stability properties of accelerating wormholes with periodic potential, introducing new insights into their horizon structure and perturbation spectra.

Findings

The wormholes lack photon orbits and shadows.

Stability analysis shows continuous spectra under standard boundary conditions.

Alternative boundary conditions yield quantized modes with quasi-normal behavior.

Abstract

The newly discovered Wormhole C--metric is a solution of Einstein's field equation coupled with a phantom scalar field which describes the accelerated wormholes. In the zero acceleration limit the solution reduces to an asymptotically flat wormhole. For certain range of parameter space this solution doesn't possess any horizon, thus making it a viable candidate of wormhole. To completely unveil this property we have studied the topological properties of this spacetime and shown that the throat is marginally connected. In the aforementioned range of parameters, the spacetime doesn't posses any photon orbit confirming the absence of shadow. We further analysed the stability of this spacetime under scalar perturbation. Under the usual boundary conditions (outgoing waves at both spatial infinities) there exists a continuous spectra. On the contrary one may achieve the quantization of the modes by exploiting a different but physically intuitive boundary condition. The lowest lying mode behaves as normal mode, and the imaginary part comes into play for the modes corresponding to first overtone number $(n=1)$ marking the onset of quasi-nomral modes for all azimuthal quantum number, $L$. We have also argued that the spacetime has a tendency to hold the excitation in it due to the external perturbation, rather than a fast de-excitation.