Scalar fields as sources for wormholes and regular black holes

We review nonsingular static, spherically symmetric solutions of general relativity with a minimally coupled scalar field $\phi$ as a source. Considered are wormholes and regular black holes without a center, including black universes (black holes with an expanding cosmology beyond the horizon). Such configurations require a "ghost" field with negative kinetic energy, but it may be negative in a restricted (strong-field) region of space and positive outside it ("trapped ghost") thus explaining why no ghosts are observed under usual conditions. Another possible explanation of the same may be a rapid decay of a ghost field at large radii. Before discussing particular examples, some general results are presented, such as the necessity of anisotropic matter for obtaining asymptotically flat or anti-de Sitter wormholes, no-hair and global structure theorems for black holes with scalar fields. The stability properties of scalar wormholes and regular black holes are discussed for perturbations preserving spherical symmetry. It is stressed that the effective potential $V_{eff}$ for perturbations has universal shapes near generic wormhole throats (a positive pole regularizable by a Darboux transformation) and near transition surfaces from canonical to ghost behavior of the scalar field (a negative pole at which the perturbation finiteness requirement plays a stabilizing role). It is also found that positive poles of $V_{eff}$ emerging at "long throats" (with the spherical radius $r \approx r_0 + {\rm const} \cdot x^{2n}$, $n > 1$, if $x=0$ is the throat) may be regularized by repeated Darboux transformations for some values of $n$.Comment: 29 pages, 6 figures. Some comments and 6 references adde

Scalar-tensor gravity and conformal continuations

Global properties of vacuum static, spherically symmetric configurations are studied in a general class of scalar-tensor theories (STT) of gravity in various dimensions. The conformal mapping between the Jordan and Einstein frames is used as a tool. Necessary and sufficient conditions are found for the existence of solutions admitting a conformal continuation (CC). The latter means that a singularity in the Einstein-frame manifold maps to a regular surface S_(trans) in the Jordan frame, and the solution is then continued beyond this surface. S_(trans) can be an ordinary regular sphere or a horizon. In the second case, S_(trans) proves to connect two epochs of a Kantowski-Sachs type cosmology. It is shown that, in an arbitrary STT, with arbitrary potential functions $U(\phi)$, the list of possible types of causal structures of vacuum space-times is the same as in general relativity with a cosmological constant. This is true even for conformally continued solutions. It is found that when S_(trans) is an ordinary sphere, one of the generic structures appearing as a result of CC is a traversable wormhole. Two explicit examples are presented: a known solution illustrating the emergence of singularities and wormholes, and a nonsingular 3-dimensional model with an infinite sequence of CCs.Comment: Latex2e, 13 pages, 3 bezier figure

Regular black holes sourced by nonlinear electrodynamics

The paper is a brief review on the existence and basic properties of static, spherically symmetric regular black hole solutions of general relativity, where the source of gravity is represented by nonlinear electromagnetic fields with the Lagrangian function $L$ depending on the single invariant $f = F_{\mu\nu}F^{\mu\nu}$ or on two variables: either $L(f, h)$, where $h = {^*}F_{\mu\nu} F^{\mu\nu}$, where ${^*}F_{\mu\nu}$ is the Hodge dual of $F_{\mu\nu}$, or $L(f, J)$, where $J = F_{\mu\nu}F^{\nu\rho} F_{\rho\sigma} F^{\sigma\mu}$. A number of no-go theorems are discussed, revealing the conditions under which the space-time cannot have a regular center, among which the theorems concerning $L(f,J)$ theories are probably new. These results concern both regular black holes and regular particlelike or starlike objects (solitons) without horizons. Thus, a regular center in solutions with an electric charge $q_e\ne 0$ is only possible with nonlinear electrodynamics (NED) having no Maxwell weak field limit. Regular solutions with $L(f)$ and $L(f, J)$ NED, possessing a correct (Maxwell) weak-field limit, are possible if the system contains only a magnetic charge $q_m \ne 0$. It is shown, however, that in such solutions the causality and unitarity as well as dynamic stability conditions are inevitably violated in a neighborhood of the center. Some particular examples are discussed.Comment: 30 pages, 4 figures. Invited chapter for the edited book "Regular Black Holes: Towards a New Paradigm of the Gravitational Collapse'' (Ed. C. Bambi, Springer Singapore, expected in 2023

Cylindrical wormholes

It is shown that the existence of static, cylindrically symmetric wormholes does not require violation of the weak or null energy conditions near the throat, and cylindrically symmetric wormhole geometries can appear with less exotic sources than wormholes whose throats have a spherical topology. Examples of exact wormhole solutions are given with scalar, spinor and electromagnetic fields as sources, and these fields are not necessarily phantom. In particular, there are wormhole solutions for a massless, minimally coupled scalar field in the presence of a negative cosmological constant, and for an azimuthal Maxwell electromagnetic field. All these solutions are not asymptotically flat. A no-go theorem is proved, according to which a flat (or string) asymptotic behavior on both sides of a cylindrical wormhole throat is impossible if the energy density of matter is everywhere nonnegative.Comment: 13 pages, no figures. Substantial changes, a no-go theorem and 2 references adde

Trapped ghosts: a new class of wormholes

We construct examples of static, spherically symmetric wormhole solutions in general relativity with a minimally coupled scalar field $\phi$ whose kinetic energy is negative in a restricted region of space near the throat (of arbitrary size) and positive far from it. Thus in such configurations a "ghost" is trapped in the strong-field region, which may in principle explain why no ghosts are observed under usual conditions. Some properties of general wormhole models with the $\phi$ field are revealed: it is shown that (i) trapped-ghost wormholes are only possible with nonzero potentials $V(\phi)$; (ii) in twice asymptotically flat wormholes, a nontrivial potential $V(\phi)$ has an alternate sign, and (iii) a twice asymptotically flat wormhole which is mirror-symmetric with respect to its throat has necessarily a zero Schwarzschild mass at both asymptotics.Comment: 4.2 pages, 4 figures. Version to appear in CQ