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.

This work analyzes the particle motion in the van Stockum spacetime considering the existence of closed timelike curves (CTCs). Test particles with or without angular momentum are studied in the present geometry. It is found that only nonzero angular momentum test particles exist in the neighborhood of CTCs. The minimum particle energy and the range of backward time jump in closed timelike geodesics (CTGs) are studied within a Cauchy horizon. Finally, a general prescription for CTC and CTG has been presented with appropriate examples.