49 research outputs found

### 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