Traversable wormhole in the deformed Ho\v{r}ava-Lifshitz gravity

TL;DR

This paper discovers asymptotically flat wormhole solutions within deformed Hořava-Lifshitz gravity, showing that higher curvature terms alone cannot produce the exotic matter needed for traversability, which must be externally supplied.

Contribution

It demonstrates that higher curvature terms in deformed Hořava-Lifshitz gravity cannot replace exotic matter, highlighting the necessity of external exotic sources for traversable wormholes.

Findings

Higher curvature terms cannot substitute exotic matter.

Exotic matter behaves like phantom energy outside the vacuum.

Energy conservation holds in the spherically symmetric setting.

Abstract

Asymptotically flat wormhole solutions are found in the deformed Ho\v{r}ava-Lifshitz gravity. It turns out that higher curvature terms can not play the role of exotic matters which are crucial to form a traversable wormhole, and external exotic sources are still needed. In particular, the exotic matter behaves like phantom energy if Kehagias-Sfetsos vacuum is considered outside the wormhole. Interestingly, the spherically symmetric setting makes the matter and the higher curvature contribution satisfy four-dimensional conservation of energy in the covariant form.