Rotating vacuum wormhole

TL;DR

This paper explores the existence of slowly rotating vacuum traversable wormholes within semiclassical gravity, revealing conditions under which such solutions with differential rotation in asymptotic regions can exist.

Contribution

It introduces a linear approximation model for rotating vacuum wormholes and demonstrates the possibility of solutions with azimuthal angle dependence and different asymptotic rotations.

Findings

Rotating solutions exist with angular velocity depending only on radial coordinate.

Wormholes can connect asymptotically flat spacetimes with different rotation rates.

Such solutions are valid in the macroscopic, Plank-scale regime.

Abstract

We investigate whether self-maintained vacuum traversible wormhole can exist described by stationary but nonstatic metric. We consider metric being the sum of static spherically symmetric one and a small nondiagonal component which describes rotation sufficiently slow to be taken into account in the linear approximation. We study semiclassical Einstein equations for this metric with vacuum expectation value of stress-energy of physical fields as the source. In suggestion that the static traversible wormhole solution exists we reveal possible azimuthal angle dependence of angular velocity of the rotation (angular velocity of the local inertial frame) that solves semiclassical Einstein equations. We find that in the macroscopic (in the Plank scale) wormhole case a rotational solution exists but only such that, first, angular velocity depends on radial coordinate only and, second, the wormhole connects the two asymptotically flat spacetimes rotating with angular velocities different in asymptotic regions.