Self-Sustained Traversable Wormholes

Abstract

In this contribution, we consider self-sustained traversable wormholes, which are configurations sustained by their own gravitational quantum fluctuations. The investigation is evaluated through a variational approach with Gaussian trial wave functionals to one loop, and the graviton quantum fluctuations are interpreted as a kind of exotic energy. Since these fluctuations usually produce ultraviolet (UV) divergences, we introduce two procedures to keep them under control. The first consists of a zeta function regularization and a renormalization process that is introduced to obtain a finite one loop energy. The second approach considers the case of distorted gravity, namely, when either Gravity’s Rainbow or a noncommutative geometry is used as a tool to keep under control the UV divergences. It is shown that for every framework, the self-sustained equation will produce a Wheeler wormhole of Planckian size. Some consequences on topology change are discussed together with the possibility of obtaining an enlarged wormhole radius.