Does violation of Cosmic No-hair Conjecture guarantee the existence of Wormhole?

TL;DR

This paper explores the relationship between the cosmic no-hair conjecture and wormholes, showing that wormholes imply violation of the conjecture, but not vice versa, in both Einstein and modified gravity theories.

Contribution

It establishes a link between wormhole existence and the violation of the cosmic no-hair conjecture across different gravity theories.

Findings

Wormholes imply violation of the cosmic no-hair conjecture.

Validity of the conjecture implies non-existence of wormholes.

Re-interpretation of gravitational entropy in wormholes.

Abstract

The present work investigates the interrelation between the validity (or violation) of the cosmic no-hair conjecture and the existence (or non-existence) of wormholes, both in Einstein's Gravity and in modified gravity theories. It is found that the existence of wormholes implies a violation of the cosmic no-hair conjecture, and the validity of the cosmic no-hair conjecture implies the non-existence of wormholes but not the reverse way both in Einstein's Gravity and in modified gravity theories. We will also re-visit the gravitational entropy predictions of the wormhole and show how they are connected.