Magnetized dusty black holes and wormholes. (arXiv:2109.12670v3 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Bronnikov_K/0/1/0/all/0/1">Kirill A. Bronnikov</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Kashargin_P/0/1/0/all/0/1">Pavel E. Kashargin</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Sushkov_S/0/1/0/all/0/1">Sergey V. Sushkov</a>
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.
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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