UDC 530.12, 524.882, 524.834 Magnetic Wormholes and Regular Black Holes with Trapped Ghosts K. A. Bronnikov∗, E. V. Donskoy†, P. A. Korolev† ∗ Center of Gravitation and Fundamental Metrology VNIIMS 46, Ozyornaya str., Moscow, 119361, Russia † Institute of Gravitation and Cosmology Peoples’ Friendship University of Russia 6, Miklukho-Maklaya str., Moscow, 117198, Russia We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields which describe traversable wormholes (with flat and AdS asymptotics) and regular black holes, in particular, black universes. <...> A black universe is a nonsingular black hole where, beyond the horizon, there is an expanding, asymptotically isotropic universe. <...> The scalar field in our solutions is minimally coupled to gravity, has a nonzero self-interaction potential, while its kinetic energy is negative in a restricted strong-field region of space–time and positive outside it. <...> Thus in such configurations a “ghost” (as are called fields with negative kinetic energy) is trapped in a small part of space, and this may in principle explain why no ghosts are observed under usual conditions. <...> The configurations obtained contain different numbers of Killing horizons, from zero to four. <...> Key words and phrases: black holes, wormholes, nonsingular cosmology, phantom matter, electromagnetic field. 1. <...> Introduction Modern cosmological observations (see, e.g., [1, 2]) favor, to a certain extent, the existence of phantom matter which violates all standard energy conditions (w = p/ρ, the pressure to energy density ratio, for phantom matter is smaller than −1). <...> Various kinds of phantom matter are discussed in cosmology as possible dark energy candidates. <...> An opportunity of interest has been suggested in [4]: there can be a kind of matter which possesses phantom properties only in a restricted region of space, a strong-field region, whereas far away from it all standard energy conditions are observed. <...> As an example of such matter, it was suggested [4] to use a minimally coupled scalar field with the Lagrangian1 Ls = 1 2h(ϕ)gµν∂µϕ∂νϕ−V (ϕ), (1) where h(ϕ) and V (ϕ) are arbitrary <...>