arXiv subjects

K. A. Bronnikov

Publications and source records attributed to K. A. Bronnikov.

At least 55 records · Page 3Linked to original sources

arXiv2016

Wormholes and black universes communicated with extra dimensions

In 6D general relativity with a phantom scalar field as a source of gravity, we present solutions that implement a transition from an effective 4D geometry times small extra dimensions to an effectively 6D space-time where the physical laws are different from ours. We consider manifolds with the structure M0 x M1 x M2, where M0 is 2D Lorentzian space-time while each of M1 and M2 can be a 2-sphere or a 2-torus. Some solutions describe wormholes with spherical symmetry in our space-time and toroidal extra dimensions. Others are of black universe type: at one end there is a 6D asymptotically anti-de Sitter black hole while beyond the horizon the geometry tends to a 4D de Sitter cosmology times a small 2D spherical extra space.

gr-qc↗

arXiv2016

Cosmology in nonlinear multidimensional gravity and the Casimir effect

We study the possible cosmological models in Kaluza-Klein-type multidimensional gravity with a curvature-nonlinear Lagrangian and a spherical extra space, taking into account the Casimir energy. First, we find a minimum of the effective potential of extra dimensions, leading to a physically reasonable value of the effective cosmological constant in our 4D space-time. In this model, the huge Casimir energy density is compensated by a fine-tuned contribution of the curvature-nonlinear terms in the original action. Second, we present a viable model with slowly evolving extra dimensions and power-law inflation in our space-time. In both models, the results formulated in Einstein and Jordan frames are compared.

gr-qc↗

arXiv2016

Wormholes leading to extra dimensions

In 6D general relativity with a scalar field as a source of gravity, a new type of static wormhole solutions is presented: such wormholes connect our universe with a small 2D extra subspace with a universe where this extra subspace is large, and the whole space-time is effectively 6-dimensional. We consider manifolds with the structure M0 x M1 x M2 , where M0 is 2D Lorentzian space-time while each of M1 an M2 can be a 2-sphere or a 2-torus. After selecting possible asymptotic behaviors of the metric functions compatible with the field equations, we give two explicit examples of wormhole solutions with spherical symmetry in our space-time and toroidal extra dimensions. In one example, with a massless scalar field (it is a special case of a well-known more general solution), the extra dimensions have a large constant size at the "far end"; the other example contains a nonzero potential $V(ϕ)$ which provides a 6D anti-de Sitter asymptotic, where all spatial dimensions are infinite.

gr-qc↗

arXiv2016

Wormholes and black universes without phantom fields in Einstein-Cartan theory

We obtain a family of regular static, spherically symmetric solutions in Einstein--Cartan theory with an electromagnetic field and a nonminimally coupled scalar field with the correct sign of kinetic energy density. At different values of its parameters, the solution, being asemptotically flat at large values of the radial coordinate, describes (i) twice asemptotically flat symmetric wormholes, (ii) asymmetric wormholes with an AdS asymptotic at the "far end", (iii) regular black holes with an extremal horizon or two simple horizons, and (iv) black universes with a de Sitter asymptotic at the "far end". As in other black universe models, it is a black hole as seen by a distant observer, but beyond its horizon there is a nonsingular expanding universe. In all these cases, both the metric and the torsion are regular in the whole space.

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arXiv2016

The Birkhoff theorem and string clouds

We consider spherically symmetric space-times in GR under the unconventional assumptions that the spherical radius $r$ is either a constant or has a null gradient in the $(t,x)$ subspace orthogonal to the symmetry spheres (i.e., $(\partial r)^2 = 0$). It is shown that solutions to the Einstein equations with $r = \rm const$ contain an extra (fourth) spatial or temporal Killing vector and thus satisfy the Birkhoff theorem under an additional physically motivated condition that the lateral pressure is functionally related to the energy density. This leads to solutions that directly generalize the Bertotti-Robinson, Nariai and Plebanski-Hacyan solutions. Under similar conditions, solutions with $(\partial r)^2 = 0$ but $r\ne\rm const$, supported by an anisotropic fluid, contain a null Killing vector, which again indicates a Birkhoff-like behavior of the system. Similar space-times supported by pure radiation (in particular, a massless radiative scalar field) contain a null Killing vector without additional assumptions, which leads to one more extension of the Birkhoff theorem. Exact radial wave solutions have been found (i) with an anisotropic fluid and (ii) with a gas of radially directed cosmic strings (or a "string cloud") combined with pure radiation. Furthermore, it is shown that a perfect fluid with isotropic pressure and a massive or self-interacting scalar field cannot be sources of gravitational fields with a null but nonzero gradient of $r$.

gr-qc↗

arXiv2015

On horizons and wormholes in k-essence theories

We study the properties of possible static, spherically symmetric configurations in k-essence theories with the Lagrangian functions of the form $F(X)$, $X \equiv ϕ_{,α} ϕ^{,α}$. A no-go theorem has been proved, claiming that a possible black-hole-like Killing horizon of finite radius cannot exist if the function $F(X)$ is required to have a finite derivative $dF/dX$. Two exact solutions are obtained for special cases of k-essence: one for $F(X) =F_0 X^{1/3}$, another for $F(X) = F_0 |X|^{1/2} - 2 Λ$, where $F_0$ and $Λ$ are constants. Both solutions contain horizons, are not asymptotically flat, and provide illustrations for the obtained no-go theorem. The first solution may be interpreted as describing a black hole in an asymptotically singular space-time, while in the second solution two horizons of infinite area are connected by a wormhole.

gr-qc↗

arXiv2015

Visible, invisible and trapped ghosts as sources of wormholes and black universes

We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields, describing traversable wormholes with flat and AdS asymptotics and regular black holes, in particular, black universes. (A black universe is a regular black hole with an expanding, asymptotically isotropic space-time beyond the horizon.) Such objects exist in the presence of scalar fields with negative kinetic energy ("phantoms", or "ghosts"), which are not observed under usual physical conditions. To account for that, we consider what we call "trapped ghosts" (scalars whose kinetic energy is only negative in a strong-field region of space-time) and "invisible ghosts", i.e., phantom scalar fields sufficiently rapidly decaying in the weak-field region. The resulting configurations contain different numbers of Killing horizons, from zero to four.

gr-qc↗

arXiv2015

Rotating cylindrical wormholes: a no-go theorem

The existing solutions to the Einstein equations describing rotating cylindrical wormholes are not asymptotically flat and therefore cannot describe wormhole entrances as local objects in our Universe. To overcome this difficulty, flat asymptotic regions are added to wormhole solutions by matching them at some surfaces $Σ_-$ and $Σ_+$. It is shown, however, that if the wormhole solution is obtained for scalar fields with arbitrary potentials, possibly interacting with an azimuthal electric or magnetic field, then the matter content of one or both thin shells appearing on $Σ_-$ and $Σ_+$ violate the Null Energy Condition. Thus exotic matter is still necessary for obtaining a twice asymptotically flat wormhole.

gr-qc↗

arXiv2015

Rotating cylindrical wormholes and energy conditions

We seek wormholes among rotating cylindrically symmetric configurations in general relativity. Exact wormhole solutions are presented with such sources of gravity as a massless scalar field, a cosmological constant, and a scalar field with an exponential potential. However, none of these solutions are asymptotically flat, which excludes the existence of wormhole entrances as local objects in our Universe. To overcome this difficulty, we try to build configurations with flat asymptotic regions using the cut-and-paste procedure: on both sides of the throat, a wormhole solution is matched to a properly chosen region of flat space-time at some surfaces $Σ_-$ and $Σ_+$. It is shown, however, that if the source of gravity in the throat region is a scalar field with an arbitrary potential, then one or both thin shells appearing on $Σ_-$ and $Σ_+$ inevitably violate the null energy condition. Thus, although rotating wormhole solutions are easily found without exotic matter, such matter is still necessary for obtaining asymptotic flatness.

gr-qc↗

arXiv2015

Wormholes without exotic matter in Einstein-Cartan theory

We study the possible existence of static traversable wormholes without invoking exotic matter in the framework of the Einstein--Cartan theory. A family of exact static, spherically symmetric wormhole solutions with an arbitrary throat radius, with flat or AdS asymptotic behavior, has been obtained with sources in the form of two noninteracting scalar fields with nonzero potentials. Both scalar fields are canonical (that is, satisfy the weak energy condition), one is minimally and the other nonminimally coupled to gravity, and the latter is a source of torsion.

gr-qc↗

arXiv2015

Quasi-black holes: general features and purely field configurations

Objects that are on the threshold of forming the horizon but never collapse are called quasi-black holes (QBHs). We discuss the properties of the general spherically symmetric QBH metric without addressing its material source, including its limiting cases as the corresponding small parameter tends to zero. We then show that QBHs can exist among self-gravitating configurations of electromagnetic and dilatonic scalar fields without matter. These general results are illustrated by explicit examples of exact solutions.

gr-qc↗

arXiv2015

Magnetic wormholes and black universes with invisible ghosts

We construct explicit examples of globally regular static, spherically symmetric solutions in general relativity with scalar and electromagnetic fields describing traversable wormholes with flat and AdS asymptotics and regular black holes, in particular, black universes. (A black universe is a regular black hole with an expanding, asymptotically isotropic space-time beyond the horizon.) The existence of such objects requires invoking scalars with negative kinetic energy ("phantoms", or "ghosts"), which are not observed under usual physical conditions. To account for that, the so-called "trapped ghosts" were previously introduced, i.e., scalars whose kinetic energy is only negative in a restricted strong-field region of space-time and positive outside it. This approach leads to certain problems, including instability (as is illustrated here by derivation of an effective potential for spherical pertubations of such systems). In this paper, we use for model construction what we call "invisible ghosts", i.e., phantom scalar fields sufficiently rapidly decaying in the weak-field region. The resulting configurations contain different numbers of Killing horizons, from zero to four.

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arXiv2014

On new definitions of SI base units. Why is the "atomic" kilogram preferable

We discuss the role of fundamental constants and measurement data for the Planck, Avogadro and Boltzmann constants and the elementary electric charge in connection with the planned transition to new definitions of four base SI units (the kilogram, mole, ampere and kelvin) in terms of fixed values of these constants. It is proposed to choose a new definition of any base SI unit in terms of a particular fundamental physical constant using a number of criteria, or principles, such as succession relative to the current SI, a sufficient stability of the new unit standards, and concordance between physical dimensions of the unit and the corresponding fundamental constant. It is argued that a redefinition of the kilogram and mole by fixing the values of the atomic mass unit and the Avogadro constant satisfies all these criteria and bears some more advantages against the version with fixed Planck constant: a well founded approach to definition of the ampere and the opportunity to preserve the current relationship between definitions of the mole and the kilogram. It is also argued that the kelvin can be redefined independently of the other three units.

physics.ins-det↗

arXiv2014

Dilaton gravity, (quasi-) black holes, and scalar charge

We consider static electrically charged dust configurations in the framework of Einstein-Maxwell-dilaton gravity with the interaction term P(χ) F_{mn} F^{mn} in the Lagrangian, where P(χ) is an arbitrary function of the dilaton field χ, and the latter is allowed to be normal or phantom. It is shown that, for any regular P(χ), static configurations are possible with arbitrary functions g_{00} = e^{2γ(x^i)} (i=1,2,3) and χ= χ(γ), without any assumption of spatial symmetry. The corresponding matter, electric charge and scalar charge densities are found from the field equations. Meanwhile, configurations with nontrivial χ(x^i) generically require a nonzero scalar charge density distribution. The classical Majumdar-Papapetrou (MP) system is obtained as a special case where χ= const; there is its scalar analogue in the case F_{mn} = 0, but only with a phantom χfield. Among possible solutions are black-hole (BH) and quasi-black-hole (QBH) ones. Some general results on QBH properties obtained previously for the MP system are here extended to systems with the dilaton. Particular examples of asymptotically flat spherically symmetric BH and QBH solutions are found, some of them being phantom-free, that is, exist with positive energy densities of matter and both scalar and electromagnetic fields.

gr-qc↗

arXiv2014

Dilaton gravity, charged dust, and (quasi-) black holes

We consider Einstein-Maxwell-dilaton gravity with charged dust and interaction of the form $P(χ) F_{μν} F^{μν}$, where $P(χ)$ is an arbitrary function of the dilaton field $χ$ that can be normal or phantom. For any regular $P(χ)$, static configurations are possible with arbitrary functions $g_{00} = \exp(2γ(x^i))$ ($i=1,2,3$) and $χ= χ(γ)$, without any assumption of spatial symmetry. The classical Majumdar-Papapetrou system is restored by putting $χ=$ const. Among possible solutions are black-hole (BH) and quasi-black-hole (QBH) ones. Some general results on BH and QBH properties are deduced and confirmed by examples. It is found, in particular, that asymptotically flat BHs and QBHs can exist with positive energy densities of matter and both scalar and electromagnetic fields.

gr-qc↗

arXiv2014

Cylindrically and axially symmetric wormholes. Throats in vacuum?

This brief review discusses the existence conditions of wormhole throats and wormholes as global configurations in general relativity under the assumptions of cylindrical and axial symmetries. It is pointed out, in particular, that wormhole throats can exist in static, cylindrically symmetric space-times under slightly different conditions as compared with spherical symmetry. In cylindrical space-time with rotation, throats can exist in the presence of ordinary matter or even in vacuum; however, there are substantial difficulties in obtaining asymptotically flat wormhole configurations without exotic matter: such examples are yet to be found. Some features of interest are discussed in static, axially symmetric configurations, including wormholes with singular rings and wrongly seeming regular wormhole throats in the Zipoy-Voorhees vacuum space-time.

gr-qc↗

arXiv2013

Variations of $α$ and $G$ from nonlinear multidimensional gravity

To explain the recently reported large-scale spatial variations of the fine structure constant $α$, we apply some models of curvature-nonlinear multidimensional gravity. Under the reasonable assumption of slow changes of all quantities as compared with the Planck scale, the original theory reduces to a multi-scalar field theory in four dimensions. On this basis, we consider different variants of isotropic cosmological models in both Einstein and Jordan conformal frames. One of the models turns out to be equally viable in both frames, but in the Jordan frame the model predicts simultaneous variations of $α$ and the gravitational constant $G$, equal in magnitude. Large-scale small inhomogeneous perturbations of these models allow for explaining the observed spatial distribution of $α$ values.

gr-qc↗

arXiv2013

Example of a stable wormhole in general relativity

We study a static, spherically symmetric wormhole model whose metric coincides with that of the so-called Ellis wormhole but the material source of gravity consists of a perfect fluid with negative density and a source-free radial electric or magnetic field. For a certain class of fluid equations of state, it has been shown that this wormhole model is linearly stable under both spherically symmetric perturbations and axial perturbations of arbitrary multipolarity. A similar behavior is predicted for polar nonspherical perturbations. It thus seems to be the first example of a stable wormhole model in the framework of general relativity (at least without invoking phantom thin shells as wormhole sources).

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