Braneworld Black Bounce to Transversable Wormhole

TL;DR

This paper demonstrates how a 4D traversable wormhole geometry can be embedded into a 5D Randall-Sundrum model through bulk deformations, transforming a black hole into a regularized wormhole while analyzing stability and energy conditions.

Contribution

It introduces a method to embed Simpson Visser spacetime into a Randall-Sundrum setup via bulk deformations, leading to a regularized, stable wormhole geometry on the brane.

Findings

Transition from Schwarzschild to Simpson Visser spacetime on the brane.

Identification of conditions satisfying or violating energy conditions.

Proposal of stability analysis based on the speed of sound in the matter fields.

Abstract

We provide a way for embedding a 4-dimensional geometry corresponding to the Simpson Visser (SV) spacetime which is capable of representing a traversable wormhole, a one-way wormhole, or a regular black hole into a Randall-Sundrum setup. To achieve this, we linearly deform the bulk geometry and the bulk matter distribution concerning a coupling constant. These deformations induce a transition from a $5D$ vacuum AdS state to an anisotropic matter distribution. The latter results in the induced geometry on the brane transitioning from a singular Schwarzschild spacetime to a regularized SV spacetime. Since there are no sources or matter fields on the brane, we can assert that the induced SV geometry on the brane arises from the influence of geometrical and matter deformations in the bulk. Thus, the central singularity is suppressed. We determine the cases where the energy conditions are either satisfied or violated. Our spacetime is asymptotically radial AdS, which is intriguing given the absence of a global AdS box that would prevent instability under larger wavelength perturbations. Therefore, it is no longer appropriate to claim that instability exists for very small perturbations near the AdS horizon. Thus, we propose that the stability of the solution can be analyzed by examining the speed of sound due to the presence of matter fields in the energy momentum tensor.