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arXiv · 2109.12670

Magnetized dusty black holes and wormholes

Kirill A. Bronnikov·Pavel E. Kashargin·Sergey V. Sushkov
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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.

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Kirill A. Bronnikov, Pavel E. Kashargin, Sergey V. Sushkov. 2021-09-26. Magnetized dusty black holes and wormholes. https://arxiv.org/abs/2109.12670

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