Magnetized dusty black holes and wormholes

TL;DR

This paper explores solutions to Einstein's equations describing dust clouds with magnetic fields, demonstrating conditions for wormhole formation, their properties, and potential traversability within cosmological models.

Contribution

It introduces new conditions under which wormholes can form in dust cloud models with magnetic fields and analyzes their properties and evolution.

Findings

Wormhole throats can exist in elliptic branches under specific conditions.

Throats are generally located in T-regions, indicating non-traversability in certain models.

Dust clouds with throats can form finite-lived wormholes in cosmological settings.

Abstract

We consider the generalized Tolman solution of general relativity, describing the evolution of a spherical dust cloud in the presence of an external electric or magnetic field. The solution contains three arbitrary functions $f(R)$, $F(R)$ and $\tau_0(R)$, where $R$ is a radial coordinate in the comoving reference frame. The solution splits into three branches corresponding to hyperbolic ($f >0$), parabolic ($f=0$) and elliptic ($f < 0$) types of motion. In such models, we study the possible existence of wormhole throats defined as spheres of minimum radius at a fixed time instant, and prove the existence of throats in the elliptic branch under certain conditions imposed on the arbitrary functions. It is further shown that the normal to a throat is a timelike vector (except for the instant of maximum expansion, when this vector is null), hence a throat is in general located in a T-region of space-time. Thus if such a dust cloud is placed between two empty (Reissner-Nordstr\"om or Schwarzschild) space-time regions, the whole configuration is a black hole rather than a wormhole. However, dust clouds with throats can be inscribed into closed isotropic cosmological models filled with dust to form wormholes which exist for a finite period of time and experience expansion and contraction together with the corresponding cosmology. Explicit examples and numerical estimates are presented. The possible traversability of wormhole-like evolving dust layers is established by a numerical study of radial null geodesics.