It is shown that general relativity coupled to nonlinear electrodynamics (NED) with the Lagrangian $L\left(F\right),$ ${F=F}_{\mu \nu }{F}^{\mu \nu }$ having a correct weak field limit, leads to nontrivial spherically symmetric solutions with a globally regular metric if and only if the electric charge is zero and $L\left(F\right)\mathrm{}$ tends to a finite limit as $\overrightarrow{F}\infty .$ The properties and examples of such solutions, which include magnetic black holes and solitonlike objects (monopoles), are discussed. Magnetic solutions are compared with their electric counterparts. A duality between solutions of different theories specified in two alternative formulations of NED (called the $\mathrm{FP}$ duality) is used as a tool for this comparison.

We study self-gravitating, static, spherically symmetric phantom scalar fields with arbitrary potentials (favored by cosmological observations) and single out 16 classes of possible regular configurations with flat, de Sitter, and anti–de Sitter asymptotics. Among them are traversable wormholes, bouncing Kantowski-Sachs (KS) cosmologies, and asymptotically flat black holes (BHs). A regular BH has a Schwarzschild-like causal structure, but the singularity is replaced by a de Sitter infinity, giving a hypothetic BH explorer a chance to survive. It also looks possible that our Universe has originated in a phantom-dominated collapse in another universe, with KS expansion and isotropization after crossing the horizon. Explicit examples of regular solutions are built and discussed. Possible generalizations include $k$-essence type scalar fields (with a potential) and scalar-tensor gravity.

The condition $R=0,$ where R is the four-dimensional scalar curvature, is used for obtaining a large class (with an arbitrary function of $r)$ of static, spherically symmetric Lorentzian wormhole solutions. The wormholes are globally regular and traversable, can have throats of arbitrary size and can be both symmetric and asymmetric. These solutions may be treated as possible wormhole solutions in a brane world since they satisfy the vacuum Einstein equations on the brane where effective stress-energy is induced by interaction with the bulk gravitational field. Some particular examples are discussed.

We test the stability of various wormholes and black holes supported by a scalar field with a negative kinetic term. The general axial perturbations and the monopole type of polar perturbations are considered in the linear approximation. Two classes of objects are considered: (i) wormholes with flat asymptotic behavior at one end and anti-de Sitter on the other (Minkowski–anti-de Sitter wormholes) and (ii) regular black holes with asymptotically de Sitter expansion far beyond the horizon (the so-called black universes). A difficulty in such stability studies is that the effective potential for perturbations forms an infinite wall at throats, if any. Its regularization is in general possible only by numerical methods, and such a method is suggested in a general form and used in the present paper. As a result, we have shown that all configurations under study are unstable under spherically symmetric perturbations, except for a special class of black universes where the event horizon coincides with the minimum of the area function. For this stable family, the frequencies of quasinormal modes of axial perturbations are calculated.

A Comment on the Letter by Eloy Ayon-Beato and Alberto Garcia, Phys. Rev. Lett. 80, 5056 (1998).

Simpson-Visser (SV) spacetimes are the simplest globally regular modifications of the Schwarzschild, Reissner-Nordsröm and other black hole solutions of general relativity. They smoothly interpolate between these black holes and traversable wormholes. After a brief presentation of the Schwarzschild-like and Reissner-Nordsröm-like SV geometries, including their Carter-Penrose diagrams, we show that any static, spherically symmetric SV metric can be obtained as an exact solution to the Einstein field equations sourced by a combination of a minimally coupled phantom scalar field with a nonzero potential $V(\varphi )$ and a magnetic field in the framework of nonlinear electrodynamics with the Lagrangian $\mathcal{L}(F)$, $\mathcal{F}=F_{\mu \nu }{F}^{\mu \nu }$ (in standard notations). Explicit forms of $V(\varphi )$ and $\mathcal{L}(F)$ are presented for the cases of Schwarzschild-like and Reissner-Nordsröm-like SV metrics.